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

What these 12 flashcards ask

Determinant of \begin{pmatrix}a&b\\ c&d\end{pmatrix}?
When is a matrix singular?
When is a matrix non-singular?
Inverse of \begin{pmatrix}a&b\\ c&d\end{pmatrix}?
What does \mathbf{A}\mathbf{A}^{-1} equal?
What is (\mathbf{A}\mathbf{B})^{-1}?
What is (\mathbf{A}^{-1})^{-1}?
Solve \mathbf{A}\mathbf{X}=\mathbf{C} for \mathbf{X}.
Solve \mathbf{X}\mathbf{A}=\mathbf{C} for \mathbf{X}.
How do you find the values of k that make \begin{pmatrix}k&6\\2&k+1\end{pmatrix} singular?
Determinant of \begin{pmatrix}3&-2\\5&4\end{pmatrix}?
Why do singular matrices have no inverse?

Exam questions on 2x2 determinants and inverse matrices

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).