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

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

A square matrix all of whose elements except the main diagonal are zeros is called a

• Null matrix A
• Singular matrix B
• Symmetric matrix C
• Diagonal matrix D

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 0 B
• -1 C
• 2 D

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

The transport of a square matrix is a

• Row matrix A
• Column matrix B
• Square matrix C
• Null 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

• 
  A
• 
  B
• 
  C
• 
  D

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

• A A
• A' B
• -A C
• A D

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

• 3, -3, 11 A
• 3, 3, 11 B
• -3, 3, -11 C
• -3, -3, 11 D

• 0 A
• 1 B
• -A C
• -1 D

• 
  A
• 
  B
• 
  C
• 
  D

A matrix with a single column is called

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

• A^- A
• A^t B
• -A C
• A D

• 0 A
• Independent of a B
• Independent of b C
• Independent of c D

Matrix multiplication is

• Commutative A
• Not commutative B
• Not associative C
• Not distributive D

The order of the matrix [1 2 3] is

• 1 x 1 A
• 3 x 3 B
• 3 x 1 C
• 1 x 3 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• all D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 0 B
• 3 C
• -1 D

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

Cofactor of an element aij denoted by Aij is

• (-2)i+j A
• Mij B
• (-1)i+j Mij C
• None of above 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

The transpose of a column matrix is a ______

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

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

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