Determinants - Expansion, Properties

Grade 12 Maths Higher — Determinants - Expansion, Properties: 25 practice questions with instant scoring and explanations.

1. The determinant of a 2×2 matrix [a b; c d] is:
2. For 3×3 matrix expansion by first row, det(A) =
3. If two rows of a matrix are identical, det(A) =
4. If matrix B is obtained by swapping two rows of A, then det(B) =
5. If matrix B = kA (scalar multiplication), then det(B) =
6. If matrix B is obtained by adding r times row i to row j of A, then det(B) =
7. For matrices A and B (same order), det(AB) =
8. For a square matrix A, det(Aᵀ) =
9. If det(A) = 5, then det(2A) for 3×3 matrix is:
10. The determinant of an identity matrix I is:
11. A square matrix A is invertible if and only if:
12. For an invertible matrix A, det(A⁻¹) =
13. If A is an upper triangular matrix, det(A) equals:
14. The determinant of a singular matrix is:
15. For an orthogonal matrix A, det(A) =
16. If det(A) = -2 and A is 2×2, then det(-A) =
17. Vandermonde determinant for x₁, x₂, x₃ equals:
18. For a permutation matrix P, det(P) =
19. If det(AB) = 6 and det(A) = 2, then det(B) =
20. The product of eigenvalues of A equals:
21. For a block matrix [A 0; 0 B], the determinant is:
22. det(Aⁿ) = [det(A)]ⁿ is true because:
23. If A is 4×4 with det(A) = 8, then det(A²) =
24. The Cauchy-Binet formula relates determinants of:
25. Review question for Determinants - Expansion, Properties