Question

If matrix A has dimensions 3 x 2 and matrix B has dimensions 3 x 2, can matrix A and matrix B be multiplied?

Answer 1

Matrices can only be multiplied if their inner dimension agree.

for example

an \(n\times m\) matrix can be multiplied by a \(m\times p\) matrix,
this will produce a \(n\times p\) matrix

\[\mathrm A_{n\times m}\times \mathrm B_{m\times p} = \mathrm C_{n\times p}\]