Free Test Matrices and Determinants – JEE

Q1: What is the order of a matrix with 3 rows and 4 columns?

A. 3x3 B. 4x3 C. 3x4 D. 4x4

Q2: If A is a 2x2 matrix with elements [1, 2; 3, 4], what is the determinant of A?

A. -2 B. 10 C. -10 D. 2

Q3: Which matrix has the same number of rows and columns?

A. Rectangular matrix B. Square matrix C. Column matrix D. Row matrix

Q4: The identity matrix of order 3 is:

A. [1 0 0; 0 1 0; 0 0 1] B. [0 1 0; 1 0 1; 0 0 0] C. [1 1 1; 1 1 1; 1 1 1] D. [0 0 0; 0 0 0; 0 0 0]

Q5: What is the inverse of a matrix A such that A * A⁻¹ = I?

A. Transpose of A B. Determinant of A C. Adjoint of A D. A⁻¹

Q6: If A is a matrix such that A² = A, then A is called:

A. Singular B. Idempotent C. Orthogonal D. Skew-symmetric

Q7: What is the value of the determinant of a singular matrix?

A. 1 B. 0 C. -1 D. Undefined

Q8: If A and B are two matrices such that AB ≠ BA, then A and B are:

A. Symmetric B. Commutative C. Non-commutative D. Skew-symmetric

Q9: Transpose of a matrix A is denoted by:

A. A⁻¹ B. Aᵗ C. det(A) D. adj(A)

Q10: If A is a 2x2 matrix and det(A) = 0, then A is:

A. Invertible B. Non-singular C. Singular D. Identity

Q11: The adjoint of a matrix A is:

A. Inverse of A B. Transpose of A C. Cofactor matrix transposed D. Zero matrix

Q12: A matrix is symmetric if:

A. Aᵗ = -A B. Aᵗ = A C. det(A) = 1 D. A⁻¹ = Aᵗ

Q13: Which of the following is true for identity matrix I?

A. I² = 0 B. I = A⁻¹ C. I = A D. I * A = A

Q14: If A is an orthogonal matrix, then A⁻¹ = ?

A. Aᵗ B. -A C. adj(A) D. det(A)

Q15: If A is a diagonal matrix, then det(A) is:

A. Sum of diagonal elements B. Product of diagonal elements C. 0 D. 1

Q16: For any matrix A, A + Aᵗ is always:

A. Skew-symmetric B. Symmetric C. Zero D. Singular

Q17: Which matrix has all elements zero?

A. Unit matrix B. Null matrix C. Identity matrix D. Skew-symmetric matrix

Q18: What is det([[2, 3], [1, 4]])?

A. 5 B. 7 C. 8 D. 5

Q19: Which of the following is NOT true for matrix multiplication?

A. AB = BA B. A(BC) = (AB)C C. A(B + C) = AB + AC D. k(AB) = (kA)B

Q20: The determinant of a 3x3 identity matrix is:

A. 0 B. 3 C. 1 D. 9

Quiz for Matrices and Determinants