IIT JEE Maths Practice Paper 20 – Matrices and Determinants – PYQs series

1. If A = [[2, 3], [4, 5]], then |A| is:

a) 2
b) -2
c) -1
d) 10

2. If A is a 2×2 matrix such that A² = I, then A is:

a) Invertible
b) Non-invertible
c) Null matrix
d) Diagonal

3. For a 3×3 matrix A, the value of |kA| is:

a) k³|A|
b) k²|A|
c) k|A|
d) |A|

4. If A is a singular matrix, then |A| is:

a) 1
b) -1
c) 0
d) Infinite

5. If A and B are square matrices of the same order and AB = BA, then:

a) A and B are equal
b) A is symmetric
c) A and B commute
d) B is a zero matrix

6. If A is an orthogonal matrix, then A⁻¹ is:

a) A
b) Aᵀ
c) -A
d) None of these

7. The adjoint of a diagonal matrix is:

a) Same diagonal matrix
b) Zero matrix
c) Inverse matrix
d) Transpose

8. The determinant of a skew-symmetric matrix of odd order is:

a) 0
b) 1
c) -1
d) Not defined

9. Which matrix has no inverse?

a) Identity matrix
b) Orthogonal matrix
c) Singular matrix
d) Diagonal matrix

10. Which of the following is true for all invertible matrices A and B?

a) (AB)⁻¹ = A⁻¹B⁻¹
b) (AB)⁻¹ = B⁻¹A⁻¹
c) (A + B)⁻¹ = A⁻¹ + B⁻¹
d) A⁻¹ + B⁻¹ = (AB)⁻¹