3x3 determinants and inverse matricesAQA A-Level Further Maths: Mind map

Exam questions on 3x3 determinants and inverse matrices

1. The matrix $\mathbf{A}=\begin{pmatrix}1&2&0\\3&1&1\\0&2&1\end{pmatrix}$.
   State whether $\mathbf{A}$ preserves or reverses orientation, giving a reason.2 marks
2. The matrix $\mathbf{B}=\begin{pmatrix}2&0&1\\1&1&0\\0&3&1\end{pmatrix}$, for which $\det\mathbf{B}=5$.
   Find the entry in row 3, column 2 of $\mathbf{B}^{-1}$.2 marks
3. The matrix $\mathbf{C}=\begin{pmatrix}1&1&1\\1&2&3\\1&4&9\end{pmatrix}$.
   Show that $\det\mathbf{C}=2$.3 marks