Determinants and inverses: AQA A‑Level Further Maths questions

AQA A-Level Further Maths past-paper questions on C.2 Determinants and inverses, 2019–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 19 questions on Determinants and inverses, as a list

June 2025, Paper 2, Q7 (3 marks): The matrix A is defined by −   =   −   4 2 6 3 A Find a non-zero 2 × 2 matrix B such that AB = 0 [3 marks]
June 2025, AS Paper 1, Q14 (8 marks): (a) The matrices A and B are given by A = [ 4 –3] –1 1 and B = [ 5 4 ] –3 –2 14 (a) (i) Find the matrices A–1 and B–1 [2 marks] 14 (a) (ii) Hence verify that (A
June 2024, Paper 2, Q1 (1 mark): It is given that 2 1 3 5 λ –6 = 0 where λ is a constant. Find the value of λ Circle your answer. [1 mark] –28 –8 8 28
June 2024, Paper 2, Q12 (5 marks): The transformation S is represented by the matrix M = 1 –6 2 7 The transformation T is a reflection in the line y = x√ 3 and is represented by the matrix N The
June 2024, Paper 2, Q14 (10 marks): The matrix M is defined as M = 5 2 1 6 3 2k + 3 2 1 5 where k is a constant. 14 (a) Given that M is a non-singular matrix, find M–1 in terms of k [5 marks] 14 (
June 2024, AS Paper 1, Q3 (1 mark): The matrix A is such that det(A) = 2 Determine the value of det(A–1) Circle your answer. [1 mark] –2 –1 2 1 2 2
June 2023, Paper 1, Q10 (12 marks): The matrix M is defined as M = 2 −1 1 −1 −1 −2 1 2 c 2 64 3 75 where c is a real number. 10 (a) The linear transformation T is represented by the matrix M Show
June 2023, Paper 2, Q3 (1 mark): The determinant A = 1 1 1 2 0 2 3 2 1 Which one of the determinants below has a value which is not equal to the value of A? Tick (3) one box. [1 mark] 3 1 3 2 0
June 2023, Paper 2, Q8 (6 marks): A is a non-singular 2 ≤ 2 matrix and AT is the transpose of A 8 (a) Using the result (AB)T = BTAT show that (A−1)T = (AT)−1 [3 marks] 8 (b) It is given that A =
June 2023, AS Paper 1, Q9 (11 marks): The matrix M represents the transformation T and is given by M = [ 3p + 1 p + 2 12 ] p2 – 3 9 (a) In the case when p = 0 show that the image of the point (4, 5)
June 2022, Paper 1, Q7 (9 marks): The matrix M is defined as M = 1 7 −3 3 6 k + 1 1 3 2 2 664 3 775 where k is a constant. 7 (a) (i) Given that M is a non-singular matrix, find M−1 in terms of k
June 2022, AS Paper 1, Q6 (5 marks): The matrix A is given by A = 5 2 −3 4 6 (a) Find det A [1 mark] 6 (b) Find A−1 [1 mark] 6 (c) Given that AB = 9 6 5 12 and M = 2A + B find the matrix M [3 marks
November 2021, Paper 1, Q12 (14 marks): The matrix A = 1 5 3 4 −2 p 8 5 −11 2 64 3 75 , where p is a constant. 12 (a) Given that A is a non-singular matrix, find A−1 in terms of p. State any restricti
November 2021, Paper 2, Q1 (1 mark): Which of the following matrices is singular? Circle your answer. [1 mark] 1 0 0 1 1 1 2 2 0 1 1 0 1 −2 1 2
November 2021, AS Paper 1, Q10 (8 marks): Matrix A is given by A = 3 i − 1 i 2 10 (a) Show that det A = a + i where a is an integer to be determined. [2 marks] 10 (b) Matrix B is given by B = 14 − 2i b
November 2020, Paper 2, Q8 (9 marks): (a) Factorise 2a + b + x x + b x2 + b2 0 a ×a2 a + b b b2 as fully as possible. [6 marks] 8 (b) The matrix M is defined by M = 13 + x x + 3 x2 + 9 0 5 ×25 8 3 9
November 2020, AS Paper 1, Q4 (5 marks): The matrices A and B are such that A = 2 a 3 0 −2 1 and B = 1 −3 −2 4a 0 5 2 64 3 75 4 (a) Find the product AB in terms of a. [2 marks] 4 (b) Find the determina
November 2020, AS Paper 1, Q16 (4 marks): A and B are non-singular square matrices. 16 (a) Write down the product AA−1 as a single matrix. [1 mark] 16 (b) M is a matrix such that M = AB . Prove that M−1
June 2019, AS Paper 1, Q2 (1 mark): Which of the following expressions is the determinant of the matrix a 2 b 5 ? Circle your answer. [1 mark] 5a − 2b 2a − 5b 5b − 2a 2b − 5a

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