To multiply two matrices, \(A\) and \(B\), the number of columns in matrix \(A\) must be equal to the number of rows in matrix \(B\).

Dimension Rule: If \(A\) is an \(m \times n\) matrix and \(B\) is an \(n \times p\) matrix, their product \(C = A \times B\) will be an \(m \times p\) matrix.

Calculation:

Each element \(C_{ij}\) in the resulting matrix is the dot product of row \(i\) from matrix \(A\) and column \(j\) from matrix \(B\).

\(C_{ij} = \sum_{k=1}^{n} A_{ik} \times B_{kj}\)

This calculator automatically adjusts the dimensions to ensure they are compatible for multiplication.