Practice Test


1) if a and B are two matrices of the order 3 x m and 3 x n, respectively and m=n,then the order of matrics(5A-2B) is


2) if A is matrix of order m x n and B is a matrix such that AB' and B' A are both defined,then order of matrix B is


3) For any two matrices A and b, we have


4) Assuming that the sum and product given below are defined,which of the following is not true for matrices?


5) If A and B are matrices of same order,then (AB' - BA') is a


6) If A is a singular matrix, then A adj(A)


7) If A is a skew-summetric matrix of odd order,then |adj A| is equal to


8) If A be a square matrix of order n and if |A|=D and |adj A|=D',then


9) Total number of possible matrices of order 3 x 3 with each entry 2 or 0 is


10) If I is a unit matrix of order 10,then the determinant od I is equal to


11) The system of equations x + y+3z=1,2x + y + 2z=3 and 3x+ 2y+5z=3 have


12) The value of adj (adj A) is equal to


13) The value of |adj (adj A)| is equal to


14) The value of adj(adj B)| is equal to


15) The value of |adj(adj AB)| is equal to


16) The value of |(adj(adj(adj(adj A))))| is equal to


17) Statement I: If a matrix of order 2 X 2 ,commutes with every matrix of order 2 X 2,then it is scalar matrix.
Statement II : A scalar matrix of order 2 X 2 commutes with every 2 X 2 matrix.


18) Let A be a square matrix of order 3 satisfying A A'=I to
Statement I:A' A=I
Statement II : (AB)'=B' A'


19) The number of 3 X 3 non-singular matrices with four entries as 1 and all other entries as 0,is


20) If the value of a third-order determinant is 11, then the value of the determinant formed by the co-factors is


21) Which of the following matrices does not have inverse?


22) If A, B are square matrices of order 3, then:


23) Let A be an invertible matrix. Which of the
following is not true?


24) The inverse of a symmetric matrix is :


25) The inverse of a skew–symmetric matrix is :


26) The inverse of a skew–symmetric matrix of odd
order:


27) If A is a non–singular square matrix, then
|adj. A| is :


28) Let A be a square matrix all of whose entries
are integers. Then which one of the following is
true?


29) If A is a skew-symmetric matrix, then trace of A is


30) The product of two orthogonal matrices is


31) Which one of the following is true always for any two non-singular matrices A and B of same order?


32) If A is square matrix, then


33) If A is an orthogonal matrix, then


34) Which of the following is incorrect?