Adjoint and Inverse of a Matrix

Grade 12 Maths — Adjoint and Inverse of a Matrix: 25 practice questions with instant scoring and explanations.

1. The adjoint (or adjugate) of a matrix A is:
2. For a matrix A, A × adj(A) equals:
3. If A is invertible, then A⁻¹ equals:
4. A matrix A is invertible if and only if:
5. For a 2 × 2 matrix [[a, b], [c, d]], the adjoint is:
6. If A is a 2 × 2 matrix with det(A) = 5 and adj(A) = [[3, 2], [1, 4]], then A⁻¹ equals:
7. For the matrix A = [[1, 2], [3, 4]], the determinant is:
8. For matrix A = [[1, 2], [3, 4]], the adjoint is:
9. If A⁻¹ exists, then (A⁻¹)⁻¹ equals:
10. For matrices A and B, if AB = I, then B is called:
11. The adjoint of a 3 × 3 matrix is a matrix of:
12. If A is a singular matrix, then:
13. For an invertible matrix A: (A⁻¹)^T equals:
14. The adjoint of the identity matrix I is:
15. If det(A) = d ≠ 0, then det(A⁻¹) equals:
16. For matrix A with adj(A) = B, we have det(B) equals:
17. If A is a 3 × 3 invertible matrix, then the number of cofactors to compute is:
18. The rank of an invertible n × n matrix is:
19. For a 2 × 2 matrix A = [[a, b], [c, d]], adj(A)^T equals:
20. If A⁻¹ = [[2, 3], [1, 2]], then the determinant of A⁻¹ is:
21. The property A × adj(A) = det(A) × I holds for:
22. For a diagonal matrix D with diagonal elements d₁, d₂, ..., dₙ (all non-zero), D⁻¹ has diagonal elements:
23. If A is an upper triangular matrix with non-zero diagonal elements, then A⁻¹ is:
24. The adjoint of a 2 × 2 zero matrix is:
25. Question?