Question

Let a matrix $A$ is both symmetric and skew-symmetric then the matrix $A$ is

• A. a null matrix
• B. a unit matrix
• C. a diagonal matrix
• D. a triangular matrix

Answer 1

The correct option is A a null matrix

Given a matrix $A$ is both symmetric and skew-symmetric.

Since $A$ is symmetric then $A^T=A$.....(1).

Also $A$ is skew-symmetric then $A^T=-A$.....(2).

Using (1) in (2) we get,

$A=-A$

or, $2A=O$ [ Where $O$ is the null matrix of order same as order of $A$]

or, $A=O$.

So $A$ is a null matrix.