# Matrices - Online Test

Q1. A square matrix A is called idempotent if
Explaination / Solution:

If the product of any square matrix with itself is the matrix itself , then the matrix is called Idempotent.

Q2. If is a square root of the  identity matrix, then a, b, c satisfy the relation
Explaination / Solution:

acbaacba=1001a2+bc=1
Q3.

If A and B are invertible matrices of the same order, then is equal to

Explaination / Solution:

By the property of inverse is equal to .

Q4. If , then
Explaination / Solution:

If any row or column of a square matrix is 0 , then its product with itself is always a zero matrix.

Q5. If
Explaination / Solution:

If any row or column of a square matrix is 0 , then its product with itself is always a zero matrix.

Q6. Let A be any  matrix, then  can be found only when
Explaination / Solution:

The product of any matrix with itself can be found only when it is a square matrix.i.e. m=n.

Q7. If A and B are any two matrices, then
Explaination / Solution:

Let matrix A is of order m x n , and matrix B is of order p x q . then , the product AB is defined only when n = p. that’s why, If A and B are any two matrices, thenAB may or may not be defined.

Q8.

A square matrix A =  is called a lower triangular matrix if  for

Explaination / Solution:

Lower triangular matrix is given by : Here, ${a}_{ij}=0$ , if i is less than j.and  , if i is greater than j.

Q9. A square matrix is called an upper triangular if  for
Explaination / Solution:

Upper Triangular matrix is given by : Here,  if i is greater than j.and , if I is less than j.

Q10. If, then for all natural numbers n,  is equal to
Explaination / Solution: