Add matrix multiplication function with validation

DIRECTORY.md

@@ -974,6 +974,7 @@
   * [Largest Square Area In Matrix](matrix/largest_square_area_in_matrix.py)
   * [Matrix Based Game](matrix/matrix_based_game.py)
   * [Matrix Class](matrix/matrix_class.py)
+  * [Matrix Diagonal Sum](matrix/matrix_diagonal_sum.py)
   * [Matrix Equalization](matrix/matrix_equalization.py)
   * [Matrix Multiplication Recursion](matrix/matrix_multiplication_recursion.py)
   * [Matrix Operation](matrix/matrix_operation.py)

matrix/matrix_diagonal_sum.py

@@ -0,0 +1,66 @@
+"""
+Matrix Multiplication Algorithm
+
+This function performs matrix multiplication on two valid matrices.
+It follows the mathematical definition:
+If A is an m×n matrix and B is an n×p matrix,
+then their product C is an m×p matrix.
+
+Raises:
+    ValueError: if matrices have invalid structure or incompatible sizes.
+
+Sources:
+    https://en.wikipedia.org/wiki/Matrix_multiplication
+
+Examples:
+    >>> A = [[1, 2], [3, 4]]
+    >>> B = [[5, 6], [7, 8]]
+    >>> matrix_multiply(A, B)
+    [[19, 22], [43, 50]]
+
+    >>> matrix_multiply([[1, 2, 3]], [[4], [5], [6]])
+    [[32]]
+
+    # Invalid structure
+    >>> matrix_multiply([[1, 2], [3]], [[1, 2]])
+    Traceback (most recent call last):
+    ...
+    ValueError: Invalid matrix structure
+
+    # Incompatible sizes
+    >>> matrix_multiply([[1, 2]], [[1, 2]])
+    Traceback (most recent call last):
+    ...
+    ValueError: Incompatible matrix sizes
+"""
+
+from typing import List
+
+
+def matrix_multiply(A: List[List[float]], B: List[List[float]]) -> List[List[float]]:
+    if not _is_valid_matrix(A) or not _is_valid_matrix(B):
+        raise ValueError("Invalid matrix structure")
+
+    rows_A = len(A)
+    cols_A = len(A[0])
+    rows_B = len(B)
+    cols_B = len(B[0])
+
+    if cols_A != rows_B:
+        raise ValueError("Incompatible matrix sizes")
+
+    result = [[0.0 for _ in range(cols_B)] for _ in range(rows_A)]
+
+    for i in range(rows_A):
+        for j in range(cols_B):
+            for k in range(cols_A):
+                result[i][j] += A[i][k] * B[k][j]
+
+    return result
+
+
+def _is_valid_matrix(M: List[List[float]]) -> bool:
+    if not isinstance(M, list) or not M:
+        return False
+    first_length = len(M[0])
+    return all(isinstance(row, list) and len(row) == first_length for row in M)