About Matrix Multiplication

Matrix multiplication involves multiplying two matrices \( A \) (of size \( m \times n \)) and \( B \) (of size \( n \times p \)) to produce a result matrix of size \( m \times p \). The formula for each element \( c_{ij} \) in the result matrix is:

• \( c_{ij} = \sum_{k=1}^{n} a_{ik} \cdot b_{kj} \)

For example, for \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \), the result is \( \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix} \).