Properties of Determinants

Grade 12 Maths — Properties of Determinants: 25 practice questions with instant scoring and explanations.

1. If a row (or column) of a matrix is multiplied by a scalar k, then determinant is:
2. If two rows (or columns) of a matrix are swapped, determinant:
3. If a row is added to another row multiplied by a scalar, determinant:
4. If two rows of a matrix are identical, det(A) equals:
5. For matrices A and B: det(A + B) equals:
6. For matrices A and B: det(AB) equals:
7. If A is invertible, then det(A⁻¹) equals:
8. For a scalar k and n × n matrix A: det(kA) equals:
9. If det(A) = d and det(B) = e, then det(AB) equals:
10. If a multiple of one row is added to another row, the determinant:
11. A matrix A is non-singular if and only if:
12. If all elements of a row are zero, then det(A) equals:
13. The determinant of a matrix product equals:
14. For an upper triangular matrix, determinant equals:
15. If matrix B is obtained from A by adding 2 times row 1 to row 2, then:
16. If all entries of a column are proportional to entries of another column, then det(A):
17. Swapping rows i and j multiplies determinant by:
18. If det(A) = 3 and det(B) = 4, then det(AB) equals:
19. The determinant of the identity matrix is:
20. If matrix C = 3A where A is 2 × 2, and det(A) = 2, then det(C) equals:
21. A square matrix is invertible if and only if its determinant is:
22. If two columns of a matrix are equal, then determinant equals:
23. For matrix A, det(A) = det(A^T) is:
24. The multiplicative property states: det(ABC) equals:
25. Question?