Matrices Practice Questions for GATE

Matrices Practice Questions for GATE aspirants. Try out these questions and leave your solutions and queries in the comment area

Q1) If A is an orthogonal matrix, then A-1 equals

  1. A
  2. AT
  3. A2
  4. None of these

Q2) Let A be a square matrix of order 'n' and  denotes det(A), then det(2A) is equal to

Q3) If a square matrix A satisfies the equation  then  is equal to

Q4) The matrix  has one eigen value equal to 3. The sum of the other two eigen values is

  1. p
  2. p-1
  3. p-2
  4. p-3

Q5) Let A and B be two square matrices of the same order and the rank of  is n, then the rank of AB is

  1. n
  2. n-1
  3. n+1
  4. none of these

Q6) The trace and determinant of 2x2 matrix are knwon to be -2 and -35 respectively. Its eigenvalues are

  1. -30 and -5
  2. -37 and -1
  3. -7 and 5
  4. 17.5 and -2

Q7) If  and , then  is equal to

  1. none of these

Q8) If A is a non-zero column matrix of order 4x1 and B is a non-zero row matrix of order 1x3, then the rank of matrix AB equals ______.

Q9) The eigenvalues of the matrix A given below are 15, 3 and 0. . Determinant of the matrix A is _______.

Q10) For any two 2x2 symmetric matrices A and B consider the following statements:

  1. (A+B) is a symmetric matrix
  2. (AB) is a symmetric matrix
  3. AB=(BA)T
  4. ATB=ABT

Of these statements

  1. 2,3 and 4 are correct
  2. 1,3 and 4 are correct
  3. 1 and 2 are correct
  4. 1,2,3 and 4 are correct