Matrix multiplication definition for JEE

Formula

If \(A\) is of order \(m\times n\) and \(B\) is of order \(n\times p\), then \(AB\) is of order \(m\times p\) and \((AB)_{ij}=\sum_{k=1}^{n} a_{ik}b_{kj}\).

Variables: \(A=[a_{ik}],\ B=[b_{kj}]\).

Conditions: Number of columns of \(A\) equals number of rows of \(B\).

Product evaluation, matrix equations, linear systems.