QUESTIONS ON SYMMETRIC AND SKEW SYMMETRIC MATRIX

About "Questions on Symmetric and Skew Symmetric Matrix"

Questions on Symmetric and Skew Symmetric Matrix :

Here we are going to see some practice questions on symmetric and skew symmetric matrix.

What is symmetric and skew symmetric matrix ?

A square matrix A is said to be symmetric if A^T = A.

A square matrix A is said to be skew-symmetric if A^T = −A.

Let us look into some problems to understand the concept.

Question 1 :

Construct the matrix A  =  [a_ij]_3x3, where a_ij  =  i - j. State whether A is symmetric or skew-symmetric

Solution :

From the given question, we come to know that we have to construct a matrix with 3 rows and 3 columns.

So, the matrix A with order 3 x 3 is

Now let us check whether it is symmetric or skew symmetric matrix.

Hence it is skew symmetric matrix.

Question 2 :

Let A and B be two symmetric matrices. Prove that AB = BA if and only if AB is a symmetric matrix.

Solution :

If A and B are symmetric matrices, then 

A^T  =  A and B^T  =  B

From the given question, we have to understand that we have to prove AB  =  BA if AB is symmetric matrix.

If AB is symmetric matrix, then we have to prove AB  =  BA. So, let us prove them as two cases.

After having gone through the stuff given above, we hope that the students would have understood "Questions on Symmetric and Skew Symmetric Matrix".

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