Matrix arithmeticEdexcel International A Level Further Maths: Mind map

Exam questions on Matrix arithmetic

1. $\mathbf{A}=\begin{pmatrix}2&-1\\ 3&4\end{pmatrix}$ and $\mathbf{B}=\begin{pmatrix}1&0\\ -2&5\end{pmatrix}$.
   Find $\mathbf{AB}$.2 marks
2. $\mathbf{M}=\begin{pmatrix}1&2\\ 0&-1\end{pmatrix}$ and $\mathbf{N}=\begin{pmatrix}3&1\\ 2&-2\end{pmatrix}$.
   Find $\mathbf{MN}-\mathbf{NM}$.2 marks
3. $\mathbf{P}=\begin{pmatrix}a&2\\ 1&-1\end{pmatrix}$ and $\mathbf{Q}=\begin{pmatrix}3&b\\ 0&2\end{pmatrix}$, where $a$ and $b$ are constants.
   Given that $\mathbf{P}+2\mathbf{Q}=\begin{pmatrix}10&8\\ 1&3\end{pmatrix}$, find the values of $a$ and $b$.3 marks