# Matrices - Online Test

Q1. If A and B are symmetric matrices of the same order, then
Explaination / Solution:

If A and B are symmetric matrices of the same order, then AB + BA is always a symmetric matrix.

Q2. The number of all possible matrices of order 3×3 with each entry 0 or 1 is
Explaination / Solution:

The number of elements in a 3 X 3 matrix is the product 3 X 3=9.

Each element can either be a 0 or a 1.

Given this, the total possible matrices that can be selected is 29=512

Q3.  is the matrix
Explaination / Solution:

It is an identity matrix with the order 2*2,
Q4. If P is of order 2 × 3 and Q is of order 3 × 2, then PQ is of order
Explaination / Solution:

Here, matrix P is of order  and matrix Q is of order  , then , the product PQ is defined only when : no. of columns in P = no. of rows in Q. And the order of resulting matrix is given by : rows in P x columns in Q.

Q5. The number of all the possible matrices of order 2 × 2 with each entry 0, 1 or 2 is
Explaination / Solution:

The number of elements in a 2 x 2 matrix is the product 2 x 2 =4

Each element can either be a 0,1 or 2.

Given this, the total possible matrices that can be selected is 34

Q6. If  then A is
Explaination / Solution:

A square matrix A for which, where n is a positive integer, is called a Nilpotent matrix.

The determinant and trace of the matrix is always Zero for a Nilpotent Matrix.

For the given matrix "A", determinant (A)=0 and trace(A)=0.

Q7. A square matrix  is called a diagonal matrix if  for
Explaination / Solution:

In a diagonal matrix all elements except diagonal elements are zero.i.e.

Q8. If a square matrix A has two identical rows or columns , then det.A is :
Explaination / Solution:

If two rows or column of a matrix are identical then determinant of such a matrix is zero.

Q9. The order of [x y z] is
Explaination / Solution:

. ( where ; matrix A denotes the product of three given matrices.)

Q10. If a matrix A is symmetric as well as skew symmetric then A is a
Explaination / Solution:

Only a null matrix can be symmetric as well as skew symmetric.

In Symmetric Matrix A=A,

Skew Symmetric Matrix A= -A,

Given that the matrix is satisfying both the properties therefore Equating the RHS we get A= -A i.e 2A=0 .

Therefore A=0,which is a null matrix.