Matrix arithmeticAQA A-Level Further Maths: Mind map

Exam questions on Matrix arithmetic

1. $\mathbf{C}=\begin{pmatrix}1&2\\3&4\end{pmatrix}$ and $\mathbf{D}=\begin{pmatrix}0&-1\\5&2\end{pmatrix}$.
   Given that $\mathbf{C}+\mathbf{X}=3\mathbf{I}$, where $\mathbf{I}$ is the $2\times2$ identity matrix, find $\mathbf{X}$.2 marks
2. $\mathbf{P}=\begin{pmatrix}1&0&2\\-1&3&1\end{pmatrix}$ and $\mathbf{Q}=\begin{pmatrix}2&1\\0&-1\\4&3\end{pmatrix}$.
   Find $\mathbf{PQ}$.2 marks
3. $\mathbf{M}=\begin{pmatrix}2&-1\\1&0\end{pmatrix}$.
   Find $\mathbf{M}^2$ and show that $\mathbf{M}^2=2\mathbf{M}-\mathbf{I}$, where $\mathbf{I}$ is the $2\times2$ identity matrix.3 marks