Square Matrix Multiplication Quiz

let $A$ and $B$ be two square matrcies of $3$ x $3$.

$A=\begin{bmatrix} 3 &1 &2\\ -5 &4 &1\\0&3&-8\end{bmatrix}$

$B=\begin{bmatrix} 0 &5&-1\\ 3 &2 &-1\\10&0.5&4\end{bmatrix}$

(a) What is the value of element $c_{23}$ of Matrix $C$ where $C=A$ x $B$

(b) What is the value of element $c_{23}$ of Matrix $C$ where $C=B$ x $A$

Notice that $A$ x $B\neq$$B$ x $A$, as element $c_{23}$ in
$A$ x $B$ is not the same as element $c_{23}$ in
$B$ x $A$.

Since $A$ x $B\neq$$B$ x $A$ we say they there are not commutative. This is a very interesting observation, as multiplication of scalars is definitely commutative.