Question

Disprove that the commutative property holds on the matrix multiplication.

Answer 1

For example:

$A=\begin{pmatrix} 3 & 4 \\ 1 & 2 \end{pmatrix}$

$B=\begin{pmatrix} 6 & 2 \\ 3 & 2 \end{pmatrix}$

$AB=\begin{pmatrix} 18+12 &6+8 \\ 6+6 & 2+4 \end{pmatrix}=\begin{pmatrix} 30 &14 \\ 12 & 6 \end{pmatrix}$

$BA=\begin{pmatrix} 18+2 &24+4 \\ 9+2 & 12+4 \end{pmatrix}=\begin{pmatrix} 20 &28 \\ 11 & 16 \end{pmatrix}$

$AB\neq BA$