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

If for the matrix A, A⁵= I, then A^-1=

• A² A
• A³ B
• A C
• None of above D

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

• a = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 D

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

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

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

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

• 5 A
• 
  B
• -5 C
• none D

• 
  A
• 
  B
• 
  C
• 
  D

For any positive integer n

• ABn = Bn A ⇔ AB = BA A
• ABn = Bn A⇔ A,B are square matrices and AB = BA B
• ABn = BnA⇔ A + B C
• ABn = BnA ⇔ A and B are square matries D

• 16 A
• 256 B
• 64 C
• 1024 D

An equation of the form ax + by = k is homogeneous linear equation when

• b = 0, a = 0 A
• a = 0,b ≠ 0 B
• b = -0,a≠ 0 C
• a≠ 0,b≠ 0, k = 0 D

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

Matrix multiplication is

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

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D

• 2 A
• 4 B
• 6 C
• 8 D

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

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

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

• A A
• A' B
• -A C
• A D

If there are m rows and n columns in a matrix then its order is

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

• -a -b -c A
• 1 B
• 0 C
• -1 D

• x =0, y =4 A
• x = -1, y = 2 B
• x = 2, y = 3 C
• x = 3, y = 4 D

• (2x4) A
• (2x7) B
• (2x3) C
• (7x2) D

• a²b²c² A
• 4a²b²c² B
• 4abc C
• None D

• 
  A
• 
  B
• 
  C
• 
  D

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

• 2 x 3 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D