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

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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.