Matrices Class 12 Mcq Test (120301)

If A is a skew- symmetric matrix and n is a positive integer, then Aⁿ is:

a) a symmetric matrix

b) skew–symmetric

c) diagonal matrix

d) None of these

If A is a 3×4 matrix and B is a matrix such that A’B and BA’ are both defined, then B is of the type:

a) 4×3

b) 3×4

c) 3×3 

d) 4×4

If A is a symmetric matrix and n∈N, then Aⁿ is:

a) symmetric

b) skew-symmetric

c) a diagonal matrix

d) None of these

If A is a matrix of order 3×4, then each row of A has:

a) 3 elements

b) 4 elements

c) 12 elements   

d) 7 elements

If A is a square matrix such that A² = I, then A^-1 is equal to:

a) 2A

b) 0

c) A

d) A + I

If A and B are two invertible matrices, then the inverse of AB is:

a) AB

b) BA

c) A^-1 B^-1

d) B^-1A^-1

If A is an invertible matrix, then which of the following is correct?

a) A^-1 is multi-valued

b) A^-1 is singular

c) \({(A^{-1})^T}\ne{(A^T)^{-1}}\)

d) \(|A|\ne {0}\)

If A is an m×n matrix such that AB and BA are both defined, then B is an:

a) m×n matrix

b) n×m matrix

c) n×n matrix

d) m×m matrix

If A, B are symmetric matrices of the same order, then the matrix AB – BA is:

a) 0

b) symmetric                

c) I

d) skew–symmetric

If a matrix A is symmetric as well as skew-symmetric then:

a) A is a diagonal matrix

b) A is a null matrix

c) A is a unit matrix

d) A is a triangular matrix