2x2 determinants and inverse matricesAQA A-Level Further Maths: Mind map

Exam questions on 2x2 determinants and inverse matrices

1. The matrix $\mathbf{A}=\begin{pmatrix}3&-2\\5&4\end{pmatrix}$.
   The point $P$ is mapped to the point $(4,14)$ by the transformation with matrix $\mathbf{A}$. Use the inverse of $\mathbf{A}$ to find the coordinates of $P$.2 marks
2. The matrix $\mathbf{B}=\begin{pmatrix}k&6\\2&k+1\end{pmatrix}$, where $k$ is a constant.
   Given that $k=2$, find $\mathbf{B}^{-1}$.2 marks
3. The matrices $\mathbf{P}=\begin{pmatrix}2&1\\3&2\end{pmatrix}$ and $\mathbf{Q}=\begin{pmatrix}1&-1\\0&2\end{pmatrix}$.
   Show that $\mathbf{P}$ is non-singular and find $\mathbf{P}^{-1}$.3 marks