Matrix Multiplication & Properties

Grade 12 Maths Higher — Matrix Multiplication & Properties: 25 practice questions with instant scoring and explanations.

1. If A is 2×3 and B is 3×4, the element (AB)₂₃ is obtained by:
2. For matrices, (A+B)C = AC + BC shows matrix multiplication is _____ over addition:
3. If A is 3×2, B is 2×3, and C is 3×2, then A(BC) is:
4. Matrix multiplication satisfies:
5. If AB = AC, which conclusion is valid?
6. For square matrices, (AB)² equals:
7. If A is idempotent (A² = A), then A³ =
8. If A is involutory (A² = I), then A⁴ =
9. For compatible matrices, (kA)B = k(AB) = A(kB) shows that scalar multiplication:
10. If A is m×n, then AᵀA is:
11. For matrix multiplication, which is NOT generally true?
12. If AB = I and BA = I, then B is:
13. The power A⁵ for matrix A requires:
14. If A² = A and B² = B, then (AB)² = AB requires:
15. For a matrix equation AX = B, the solution X exists and is unique when:
16. If A = [1 2; 3 4] and B = [0 1; 1 0], then AB - BA is:
17. The product of two upper triangular matrices is:
18. If A and B are symmetric and AB = BA, then AB is:
19. For matrix exponentiation, A² = A implies:
20. The commutator [A,B] = AB - BA for matrices A and B is:
21. If AB = 0 and A is invertible, then:
22. For a diagonal matrix D, DᵏD = D^(k+1) because diagonal matrices:
23. The trace function satisfies tr(AB) = tr(BA) because:
24. If A is nilpotent of order 2 (A² = 0), then (I - A)⁻¹ =
25. Review question for Matrix Multiplication & Properties