Matrices questions
472 published questions with worked solutions.
- Consider the following in respect of non-singular matrices A and B : I. (AB)^ -1 =A^ -1 B^ -1 II. (BA)(AB)^ -1 =I, where I is the...
- Consider the following statements about the matrix M= bmatrix 71&23&48 57&28&29 65&17&48 bmatrix : Statement-I : The inverse of M...
- If vmatrix a-b&p-q&x-y -c&q-r&y-z -a&r-p&z-x vmatrix =k vmatrix a&b&c &q&r &y&z vmatrix , then what is the value of k?
- Consider the following statements : I. If n n (n>1) matrix is symmetric, then its inverse is also a symmetric matrix. II. If n n...
- If M= bmatrix 2&0&0 0&2&0 0&0&2 bmatrix , then what is the value of |M| ,| adj M|?
- If M^T is the transpose of a 2 2 matrix M, then which of the following is/are correct? I. |M+M^T|=|M|+|M^T| if M is symmetric....
- If A is a square matrix of order 3 and |A|=2, then what is adj ( adj A) equal to?
- If A is a square matrix of order 3 such that A( adj A)= bmatrix 64&0&0 0&64&0 0&0&64 bmatrix then what is |A| equal to?
- Let A, B and C be the square matrices of order 2 such that AB=AC. Which of the statements given below is/are correct? I. B and C...
- If A is a square matrix of order 3 and |A|=4, then what is | adj A| equal to?
- Let A and B be symmetric matrices of the same order. Which of the following statements is/are correct? I. (AB-BA) is also a...
- If A= bmatrix -1&2 3&-4 bmatrix , then what is |A^ -1 | equal to?
- Let A= pmatrix 1&- &1 pmatrix and B= pmatrix 1& - &1 pmatrix If C=AB^ -1 , then what is (C) equal to?
- If A and B are two matrices such that AB is of order n n, then which one of the following is correct?
- If A= bmatrix 1 & a 0 & 1 bmatrix where a N , then what is A^ 100 -A^ 50 -2A^ 25 equal to, where I is the identity matrix?
- The inverse of a matrix A is given by bmatrix -2 & 1 3 2 & - 1 2 bmatrix What is A equal to?
- Let A= bmatrix 0 & 2 -2 & 0 bmatrix and (mI+nA)^2=A where m, n are positive real numbers and I is the identity matrix. What is...
- Consider the following in respect of the matrix A= bmatrix 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 bmatrix 1. Inverse of A does not exist...
- Let M be a 3 3 invertible matrix with real entries and let I denote the 3 3 identity matrix. If M^ -1 = adj ( adj M), then which...
- Let p, q, r be nonzero real numbers that are, respectively, the 10^ th , 100^ th and 1000^ th terms of a harmonic progression....
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