Class 12 Mathematics: Matrices and Determinants Practice
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Q1 · MCQ · 1 mark
If A is a square matrix of order 3 such that |adj A| = 64, then |A| is equal to:
Q2 · MCQ · 1 mark
For any two matrices A and B of suitable orders, which of the following is NOT true?
Q3 · MCQ · 1 mark
If A is a skew-symmetric matrix of odd order, then |A| is:
Q4 · MCQ · 1 mark
The number of possible matrices of order 3x3 with each entry 0 or 1 is:
Q5 · MCQ · 1 mark
If A is a non-singular matrix of order n, then adj(A)' = ?
Q6 · FILL · 1 mark
If A = [[2, -3], [4, x]] is a singular matrix, then the value of x is ____.
Q7 · FILL · 1 mark
The value of the determinant of a matrix remains unchanged if its rows and columns are ____.
Q8 · FILL · 1 mark
For an invertible matrix A, (A⁻¹)⁻¹ = ____.
Q9 · SHORT · 2 marks
If A and B are symmetric matrices of the same order, prove that AB - BA is a skew-symmetric matrix.
Q10 · SHORT · 2 marks
Without expanding, prove that for a square matrix A, |kA| = kⁿ|A| where n is the order of A.