Matrix inverse calculation

Questions requiring the calculation of the inverse of a 2×2 or 3×3 matrix, possibly in terms of parameters.

5 questions · Moderate -0.7

4.03o Inverse 3x3 matrix
Sort by: Default | Easiest first | Hardest first
Edexcel F1 2022 June Q3
4 marks Moderate -0.3
  1. \(\mathbf { M } = \left( \begin{array} { c c } k & k \\ 3 & 5 \end{array} \right) \quad\) where \(k\) is a non-zero constant
    1. Determine \(\mathbf { M } ^ { - 1 }\), giving your answer in simplest form in terms of \(k\).
    Hence, given that \(\mathbf { N } ^ { - 1 } = \left( \begin{array} { c c } k & k \\ 4 & - 1 \end{array} \right)\)
  2. determine \(( \mathbf { M N } ) ^ { - 1 }\), giving your answer in simplest form in terms of \(k\).
OCR FP1 AS 2021 June Q2
7 marks Moderate -0.8
2 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { r r c } 2 & 1 & 2 \\ 1 & - 1 & 1 \\ 2 & 2 & a \end{array} \right)\).
  1. Show that \(\operatorname { det } \mathbf { A } = 6 - 3 a\).
  2. State the value of \(a\) for which \(\mathbf { A }\) is singular.
  3. Given that \(\mathbf { A }\) is non-singular find \(\mathbf { A } ^ { - 1 }\) in terms of \(a\).
OCR MEI FP1 2007 June Q1
3 marks Moderate -0.8
You are given the matrix \(\mathbf{M} = \begin{pmatrix} 2 & -1 \\ 4 & 3 \end{pmatrix}\).
  1. Find the inverse of \(\mathbf{M}\). [2]
  2. A triangle of area 2 square units undergoes the transformation represented by the matrix \(\mathbf{M}\). Find the area of the image of the triangle following this transformation. [1]
SPS SPS FM Pure 2023 September Q1
5 marks Moderate -0.8
$$\mathbf{A} = \begin{bmatrix} 2 & 3 \\ k & 1 \end{bmatrix}$$
  1. Find \(\mathbf{A}^{-1}\) [2 marks]
  2. The determinant of \(\mathbf{A}^2\) is equal to 4. Find the possible values of \(k\). [3 marks]
SPS SPS FM Pure 2025 September Q1
5 marks Moderate -0.8
\(A = \begin{bmatrix} 2 & 3 \\ k & 1 \end{bmatrix}\)
  1. Find \(A^{-1}\) [2 marks]
  2. The determinant of \(A^2\) is equal to 4. Find the possible values of \(k\). [3 marks]