Determinants and inverses of 2x2 matricesEdexcel International A Level Further Maths: Mind map

Exam questions on Determinants and inverses of 2x2 matrices

1. $\mathbf{A}=\begin{pmatrix}4&3\\ 2&2\end{pmatrix}$.
   Given that $\mathbf{AX}=\begin{pmatrix}2&0\\ 1&1\end{pmatrix}$, find the matrix $\mathbf{X}$.2 marks
2. $\mathbf{B}=\begin{pmatrix}k&4\\ 3&k+1\end{pmatrix}$, where $k$ is a constant.
   Given that $k=2$, find $\mathbf{B}^{-1}$.2 marks
3. $\mathbf{C}=\begin{pmatrix}2&1\\ 5&3\end{pmatrix}$ and $\mathbf{D}=\begin{pmatrix}1&2\\ 1&3\end{pmatrix}$.
   Find $\mathbf{CD}$ and hence find $(\mathbf{CD})^{-1}$.3 marks