What is the correct way to multiply two matrices in Python, and what errors need to be fixed in the provided code?

Steps to Solve

1. Check Matrix Dimensions for Multiplication For matrix multiplication to be valid, the number of columns in the first matrix must equal the number of rows in the second matrix. Here, matrix1 has dimensions $3 \times 3$ (3 rows and 3 columns) and matrix2 has dimensions $2 \times 3$ (2 rows and 3 columns). Since $3 \neq 2$, matrix multiplication is not possible.

2. Correct Logical Structure of Result Initialization In the original code, the result matrix initialization is attempted but will ultimately be incorrect due to the first matrix's columns not matching the second matrix's rows. The correct initialization should follow the formula: $$ \text{result}[i][j] = 0 \text{ for } i=0...(\text{number of rows in matrix1}-1), j=0...(\text{number of columns in matrix2}-1) $$

3. Fix Nested Loop for Matrix Multiplication In a working implementation, the structure of the loops would generally follow this format:

for i in range(len(matrix1)):
    for j in range(len(matrix2[0])):
        for k in range(len(matrix2)):
            result[i][j] += matrix1[i][k] * matrix2[k][j]

This ensures that each element of the resulting matrix is computed correctly.

4. Output with Correct Variable Reference The print statement should accurately reflect outputting each row of the final result. Instead of print(rw), it should be print(row) to correctly iterate over the list of results.