diff --git a/lib/src/main/java/de/edux/core/math/matrix/classic/MatrixArithmetic.java b/lib/src/main/java/de/edux/core/math/matrix/classic/MatrixArithmetic.java
index ff809f6..a4fe389 100644
--- a/lib/src/main/java/de/edux/core/math/matrix/classic/MatrixArithmetic.java
+++ b/lib/src/main/java/de/edux/core/math/matrix/classic/MatrixArithmetic.java
@@ -1,44 +1,39 @@
 package de.edux.core.math.matrix.classic;
 
 import de.edux.core.math.IMatrixArithmetic;
-import java.util.Arrays;
+import java.util.stream.IntStream;
 
 public class MatrixArithmetic implements IMatrixArithmetic {
-  @Override
-  public double[][] multiply(double[][] matrixA, double[][] matrixB) {
-    int columnsInFirstMatrix = matrixA[0].length;
-    int rowsInSecondMatrix = matrixB.length;
-    if (columnsInFirstMatrix != rowsInSecondMatrix) {
+
+  private void checkSizeForMultiplication(double[][] matrixA, double[][] matrixB) {
+    int m = matrixB.length;
+    int n = matrixA[0].length;
+    if (m != n) {
       throw new RuntimeException(
           "\"The number of columns in the first matrix must be equal to the number of rows in the second matrix.\"");
     }
-
-    int rowsInMatrixC = matrixA.length;
-    int columnsInMatrixC = matrixB.length;
-    double[][] matrixC = new double[rowsInMatrixC][columnsInMatrixC];
-    for (int row = 0; row < rowsInMatrixC; row++) {
-      for (int column = 0; column < columnsInMatrixC; column++) {
-        matrixC[row][column] =
-            vectorDotProduct(getRowVector(matrixA, row), getColumnVector(matrixB, column));
-      }
-    }
-    return matrixC;
   }
 
-  public double[] getRowVector(double[][] matrix, int rowIndex) {
-    return matrix[rowIndex];
-  }
+  @Override
+  public double[][] multiply(double[][] matrixA, double[][] matrixB) {
+    checkSizeForMultiplication(matrixA, matrixB);
 
-  public double[] getColumnVector(double[][] matrix, int columnIndex) {
-    return Arrays.stream(matrix).mapToDouble((row) -> row[columnIndex]).toArray();
-  }
+    int aRows = matrixA.length;
+    int aColumns = matrixA[0].length;
+    int bColumns = matrixB[0].length;
 
-  public double vectorDotProduct(double[] rowVector, double[] columVector) {
-    int vectorSize = rowVector.length;
-    double vectorDotProduct = 0;
-    for (int i = 0; i < vectorSize; i++) {
-      vectorDotProduct += rowVector[i] * columVector[i];
-    }
-    return vectorDotProduct;
+    double[][] result = new double[aRows][bColumns];
+
+    IntStream.range(0, aRows)
+        .forEach(
+            row -> {
+              for (int col = 0; col < bColumns; col++) {
+                for (int i = 0; i < aColumns; i++) {
+                  result[row][col] += matrixA[row][i] * matrixB[i][col];
+                }
+              }
+            });
+
+    return result;
   }
 }
diff --git a/lib/src/main/java/de/edux/core/math/matrix/parallel/MatrixParallelArithmetic.java b/lib/src/main/java/de/edux/core/math/matrix/parallel/MatrixParallelArithmetic.java
index 2986ff3..c312fb8 100644
--- a/lib/src/main/java/de/edux/core/math/matrix/parallel/MatrixParallelArithmetic.java
+++ b/lib/src/main/java/de/edux/core/math/matrix/parallel/MatrixParallelArithmetic.java
@@ -1,10 +1,40 @@
 package de.edux.core.math.matrix.parallel;
 
 import de.edux.core.math.IMatrixArithmetic;
+import java.util.stream.IntStream;
 
 public class MatrixParallelArithmetic implements IMatrixArithmetic {
+
+  private void checkSizeForMultiplication(double[][] matrixA, double[][] matrixB) {
+    int m = matrixB.length;
+    int n = matrixA[0].length;
+    if (m != n) {
+      throw new RuntimeException(
+          "\"The number of columns in the first matrix must be equal to the number of rows in the second matrix.\"");
+    }
+  }
+
   @Override
   public double[][] multiply(double[][] matrixA, double[][] matrixB) {
-    return new double[0][];
+    checkSizeForMultiplication(matrixA, matrixB);
+
+    int aRows = matrixA.length;
+    int aColumns = matrixA[0].length;
+    int bColumns = matrixB[0].length;
+
+    double[][] result = new double[aRows][bColumns];
+
+    IntStream.range(0, aRows)
+        .parallel()
+        .forEach(
+            row -> {
+              for (int col = 0; col < bColumns; col++) {
+                for (int i = 0; i < aColumns; i++) {
+                  result[row][col] += matrixA[row][i] * matrixB[i][col];
+                }
+              }
+            });
+
+    return result;
   }
 }
diff --git a/lib/src/test/java/de/edux/core/math/matrix/parallel/MatrixParallelArithmeticTest.java b/lib/src/test/java/de/edux/core/math/matrix/parallel/MatrixParallelArithmeticTest.java
new file mode 100644
index 0000000..c1368b3
--- /dev/null
+++ b/lib/src/test/java/de/edux/core/math/matrix/parallel/MatrixParallelArithmeticTest.java
@@ -0,0 +1,157 @@
+package de.edux.core.math.matrix.parallel;
+
+import static org.junit.jupiter.api.Assertions.*;
+
+import de.edux.core.math.IMatrixArithmetic;
+import org.junit.jupiter.api.Test;
+
+class MatrixParallelArithmeticTest {
+
+  @Test
+  public void testLargeMatrixMultiplication() {
+    int matrixSize = 200;
+    double[][] matrixA = new double[matrixSize][matrixSize];
+    double[][] matrixB = new double[matrixSize][matrixSize];
+
+    for (int i = 0; i < matrixSize; i++) {
+      for (int j = 0; j < matrixSize; j++) {
+        matrixA[i][j] = 1;
+        matrixB[i][j] = 1;
+      }
+    }
+    IMatrixArithmetic matrixParallelArithmetic = new MatrixParallelArithmetic();
+    double[][] result = matrixParallelArithmetic.multiply(matrixA, matrixB);
+    for (int i = 0; i < matrixSize; i++) {
+      for (int j = 0; j < matrixSize; j++) {
+        assertEquals(matrixSize, result[i][j], "Result on [" + i + "][" + j + "] not correct.");
+      }
+    }
+  }
+
+  @Test
+  public void shouldThrowRuntimeExceptionForMatricesWithIncompatibleSizes() {
+    double[][] matrixA = {
+      {3, -5, 1},
+      {-2, 0, 4},
+      {-1, 6, 5},
+    };
+    double[][] matrixB = {
+      {7, 2, 4},
+      {0, 1, -5},
+    };
+    double[][] matrixC = {
+      {3, -5},
+      {-2, 0},
+      {-1, 6},
+    };
+
+    IMatrixArithmetic matrixParallelArithmetic = new MatrixParallelArithmetic();
+
+    assertAll(
+        () ->
+            assertThrows(
+                RuntimeException.class, () -> matrixParallelArithmetic.multiply(matrixA, matrixB)),
+        () ->
+            assertThrows(
+                RuntimeException.class, () -> matrixParallelArithmetic.multiply(matrixC, matrixA)));
+  }
+
+  @Test
+  public void shouldMultiply8x8MatricesCorrectly() {
+    double[][] matrixA = {
+      {1, 2, 3, 4, 5, 6, 7, 8},
+      {8, 7, 6, 5, 4, 3, 2, 1},
+      {2, 3, 4, 5, 6, 7, 8, 9},
+      {9, 8, 7, 6, 5, 4, 3, 2},
+      {1, 1, 1, 1, 1, 1, 1, 1},
+      {2, 2, 2, 2, 2, 2, 2, 2},
+      {1, 3, 5, 7, 9, 11, 13, 15},
+      {15, 13, 11, 9, 7, 5, 3, 1}
+    };
+    double[][] matrixB = {
+      {1, 0, 0, 0, 1, 0, 0, 0},
+      {0, 1, 0, 0, 0, 1, 0, 0},
+      {0, 0, 1, 0, 0, 0, 1, 0},
+      {0, 0, 0, 1, 0, 0, 0, 1},
+      {1, 0, 0, 0, 1, 0, 0, 0},
+      {0, 1, 0, 0, 0, 1, 0, 0},
+      {0, 0, 1, 0, 0, 0, 1, 0},
+      {0, 0, 0, 1, 0, 0, 0, 1}
+    };
+    double[][] expected = {
+      {6, 8, 10, 12, 6, 8, 10, 12},
+      {12, 10, 8, 6, 12, 10, 8, 6},
+      {8, 10, 12, 14, 8, 10, 12, 14},
+      {14, 12, 10, 8, 14, 12, 10, 8},
+      {2, 2, 2, 2, 2, 2, 2, 2},
+      {4, 4, 4, 4, 4, 4, 4, 4},
+      {10, 14, 18, 22, 10, 14, 18, 22},
+      {22, 18, 14, 10, 22, 18, 14, 10}
+    };
+
+    IMatrixArithmetic matrixParallelArithmetic = new MatrixParallelArithmetic();
+    double[][] result = matrixParallelArithmetic.multiply(matrixA, matrixB);
+
+    assertArrayEquals(
+        expected, result, "The 8x8 matrix multiplication did not yield the correct result.");
+  }
+
+  @Test
+  public void shouldMultiplyWithZeroMatrix() {
+    double[][] matrixA = {
+      {0, 0},
+      {0, 0}
+    };
+    double[][] matrixB = {
+      {1, 2},
+      {3, 4}
+    };
+    double[][] expected = {
+      {0, 0},
+      {0, 0}
+    };
+
+    IMatrixArithmetic matrixParallelArithmetic = new MatrixParallelArithmetic();
+    double[][] result = matrixParallelArithmetic.multiply(matrixA, matrixB);
+
+    assertArrayEquals(expected, result);
+  }
+
+  @Test
+  public void shouldMultiplyWithIdentityMatrix() {
+    double[][] matrixA = {
+      {1, 0},
+      {0, 1}
+    };
+    double[][] matrixB = {
+      {5, 6},
+      {7, 8}
+    };
+
+    IMatrixArithmetic matrixParallelArithmetic = new MatrixParallelArithmetic();
+    double[][] result = matrixParallelArithmetic.multiply(matrixA, matrixB);
+
+    assertArrayEquals(matrixB, result);
+  }
+
+  @Test
+  public void shouldMultiplySmallMatricesCorrectly() {
+    double[][] matrixA = {
+      {1, 2},
+      {3, 4}
+    };
+    double[][] matrixB = {
+      {2, 0},
+      {1, 2}
+    };
+    double[][] expected = {
+      {4, 4},
+      {10, 8}
+    };
+
+    IMatrixArithmetic matrixParallelArithmetic = new MatrixParallelArithmetic();
+    double[][] result = matrixParallelArithmetic.multiply(matrixA, matrixB);
+
+    assertArrayEquals(expected, result);
+  }
+}