Matrix Multiplication Practice Questions

Work out $A\begin{pmatrix} 5 \\ 2 \end{pmatrix}$

$$AN = A$$

Write down matrix $N$.

Work out
$$\begin{pmatrix} 2 & 3 \\ -1 & 4 \end{pmatrix}\begin{pmatrix} 5 & 0 \\ -2 & 1 \end{pmatrix}$$

Work out $4A$.

Work out $4A - 2B$.

Show that
$$\begin{pmatrix} 3 & 5 \\ 1 & 2 \end{pmatrix}\begin{pmatrix} 6 & -15 \\ -3 & 9 \end{pmatrix} = kI$$
where $k$ is an integer.

$$\begin{pmatrix} 4 & 3 \\ 2 & 2n \end{pmatrix}\begin{pmatrix} m & -1 \\ 2 & 5 \end{pmatrix} = \begin{pmatrix} -2 & 11 \\ 0 & 8 \end{pmatrix}$$

Work out the values of $m$ and $n$.

Work out $M^2$.

Work out $M^3$.

You may use your answer to part (a).

Work out $AB$.

Work out $BA$.

Ellie says,

"For any two $2 \times 2$ matrices, $AB$ is always the same as $BA$."

Use your answers to parts (a) and (b) to explain why Ellie is wrong.