Multiplication of Two Matrices

Tips – Multiplication of Two Matrices

• Two matrices \(A\) and \(B\) could only be multiplied, \(A \times B\) or \(AB\),

\(\quad\,\) if numbers of columns of \(A =\) number of rows of \(B\).

\(\quad\,\) If \(A\) is a \(m \times n\) matrix and \(B\) is an \(n \times b\), the result product will be a \(m \times b\) matrix.

\(\quad\,\) Example: \(\begin{pmatrix} 2 & 3 \end{pmatrix} \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} = \begin{pmatrix} 11 & 16 \end{pmatrix}\)

• Matrix multiplication is not commutative in general: even when both products are defined, \(AB\) need not equal \(BA\). Some pairs do commute, for example a square matrix and the identity matrix.