JEE MATHS UNIT 3
QUIZ NO 2
TOTAL QUESTIONS = 20
1. If A is a 2x2 matrix with det(A) = 3, then det(2A) is
A. 6
B. 9
C. 12
D. 36
2. The determinant of the matrix [[1, 2], [2, 4]] is
A. 0
B. 4
C. 2
D. 8
3. If A and B are 2x2 matrices, then det(AB) is equal to
A. det(A) + det(B)
B. det(A) - det(B)
C. det(A) * det(B)
D. det(A)/det(B)
4. The rank of a null matrix is
A. 0
B. 1
C. 2
D. undefined
5. If A is an invertible matrix, then det(A^-1) is
A. det(A)
B. 1/det(A)
C. -det(A)
D. det(A)^2
6. The determinant of a diagonal matrix is equal to
A. 0
B. 1
C. sum of diagonal elements
D. product of diagonal elements
7. If A is a square matrix such that A^2 = A, then A is called
A. identity matrix
B. zero matrix
C. idempotent matrix
D. symmetric matrix
8. The adjoint of a diagonal matrix is
A. a diagonal matrix
B. a scalar
C. a zero matrix
D. not defined
9. If A is a 3x3 matrix with det(A) = -5, then det(A^T) is
A. -5
B. 5
C. 0
D. 1
10. The determinant of a skew-symmetric matrix of even order is
A. always positive
B. always negative
C. always zero
D. nonzero
11. If A = [[1, 2], [3, 4]], then the trace of A is
A. 1
B. 2
C. 4
D. 5
12. The determinant of [[0, 1], [-1, 0]] is
A. -1
B. 0
C. 1
D. 2
13. The inverse of a matrix exists if and only if
A. the determinant is nonzero
B. the determinant is zero
C. the trace is zero
D. it is symmetric
14. If A is a 2x2 matrix with det(A) = 4, then det(3A) is
A. 12
B. 36
C. 108
D. 144
15. The product of the eigenvalues of a square matrix A is equal to
A. det(A)
B. trace(A)
C. rank(A)
D. sum of diagonal elements
16. If A is a 2x2 invertible matrix, then det(adj(A)) is
A. det(A)
B. det(A)^2
C. 1/det(A)
D. det(A)^-2
17. If A = [[2, 3], [4, 5]], then adj(A) is
A. [[5, -3], [-4, 2]]
B. [[5, -4], [-3, 2]]
C. [[2, -3], [-4, 5]]
D. [[2, 3], [4, 5]]
18. The determinant of the identity matrix of any order is
A. 0
B. 1
C. order of the matrix
D. none of these
19. If A is a square matrix, then det(kA) for a scalar k is equal to
A. k * det(A)
B. k^2 * det(A)
C. k^n * det(A)
D. det(A)/k
20. The rank of a 3x3 identity matrix is
A. 1
B. 2
C. 3
D. 0
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