Calculate the determinant and multiplicative inverse of 2 × 2 matrices, with and without technology. If 𝑨 = [𝑎 𝑏 𝑐 𝑑] then det(𝑨) = 𝑎𝑑 − 𝑏𝑐 𝑨−1 = [𝑎 𝑏 𝑐 𝑑]−1 = 1 det(𝑨) [ 𝑑 −𝑏 −𝑐 𝑎 ], det(𝑨) ≠ 0

Let \(\mathbf{A} = \begin{bmatrix} 5 & 2 \\ 3 & 4 \end{bmatrix}\) and \(\mathbf{B} = \begin{bmatrix} 4 & -2 \\ -3 & 5 \end{bmatrix}\). Calculate \(\det(\mathbf{A}) + \det(\mathbf{B})\).

A matrix \(\mathbf{A}\) is shown below. Calculate the determinant of \(\mathbf{A}\).

A transformation matrix \(\mathbf{M}\) and a point matrix \(\mathbf{P}\) are defined in the table below. (a) Calculate \(\det(\mathbf{M})\). (1 mark) (b) Determine \(\mathbf{M}^{-1}\). (2 marks) (c) Hence calculate \(\mathbf{M}^{-1}\mathbf{P}\). (1 mark)