Q. 315.0( 2 Votes )

Write a square ma

Answer :

We must understand what symmetric matrix is.

A symmetric matrix is a square matrix that is equal to its transpose.


A symmetric matrix A = AT


Now, let us understand what skew-symmetric matrix is.


A skew-symmetric matrix is a square matrix whose transpose equals its negative, that, it satisfies the condition


A skew symmetric matrix AT = -A


And,


A square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n.


We need to find a square matrix which is both symmetric as well as skew symmetric.


Take a 2 × 2 null matrix.


Say,



Let us take transpose of the matrix A.


We know that, the transpose of a matrix is a new matrix whose rows are the columns of the original.


So,



Since, A = AT.


, A is symmetric.


Take the same matrix and multiply it with -1.





Let us take transpose of the matrix –A.


So,



Since,


AT = -A


, A is skew-symmetric.


Thus, A (a null matrix) is both symmetric as well as skew-symmetric.


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