ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 5

If A is a skew-symmetric matrix of order n and P, any square matrix of order n.prove that P' AP is

• Skew-symmetric A
• Symmetric B
• Null C
• Diagonal D

• Zero matrix A
• Diagonal matrix B
• Column matrix C
• Scalar matrix D

• 
  A
• 
  B
• 
  C
• 
  D

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

• 
  A
• 
  B
• 
  C
• 
  D

• Identity matrix A
• Diagonal matrix B
• Null matrix C
• Hermitian matrix D

• Diagonal matrix A
• Scalar matrix B
• Triangular matrix C
• Identity matrix D

• Square matrix A
• Row matrix B
• Symmetric matrix C
• Null matrix D

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

• 2 AB A
• 2 BA B
• A + B C
• AB D

If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

• m x m A
• m x n B
• n x n C
• n x m D

The square matrix A is skew Hermitian when (A)'=

• A A
• A' B
• -A C
• A D

In order of A is m x n and order of B is n x p then order of AB is

• m x m A
• n x n B
• m x p C
• p x m D

If A is skew Hermitian Matrix then which of the following is not skew Hermitian matrix

• A2 A
• A5 B
• A3 C
• A7 D

If A is a non-singular matrix then adj A is

• Non-singular A
• Symmetric B
• Singular C
• Non defined D

A and B be two square matrices and if their inverse exist the (AB)-1 =

• A-1 B-1 A
• AB-1 B
• A-1B C
• B-1A-1 D

A = [3] is a/an

• Square matrix A
• Scalar matrix B
• Diagonal matrix C
• Identity matrix D

• 3 x 2 A
• 2 x 3 B
• 3 x 3 C
• 2 x 2 D

• 
  A
• 
  B
• 
  C
• 
  D

• Diagonal matrix A
• Scalar matrix B
• Triangular matrix C
• Identity matrix D

• A A
• -A B
• A^t C
• A^- D

A matrix with a single row is called a

• Column matrix A
• Row matrix B
• Null matrix C
• Identity matrix D

A square matrix A = [aij] is lower triangular matrix when:

• aij = 0 for all i < j A
• bij = 0 B
• cij = 0 C
• dij =0 D

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent D

• At A
• -A B
• A C
• A-1 D

• 
  A
• 
  B
• 
  C
• 
  D

We also the system of non-homogeneous linear equations by

• a and b A
• b and c B
• c and a C
• a, b and c D

If the trace of matrix A is 5, then the trace of the matrix 3A is

• 3/5 A
• 5/3 B
• 8 C
• 15 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is

• 1 x 1 A
• 1 x 10 B
• 10 x 10 C
• 10 x 1 D

• I3 A
• rI3 B
• r C
• none D