Question

A square matrix A is said to be a symmetric matrix if

• A. $A=-A^T$
• B. $A=A^T$
• C. $A=\overline{A}$
• D. $A=-\overline{A}$

Answer 1

The correct option is B

$A=A^T$

We have discussed that a square matrix A is called as symmetric matrix if the matrix is equal to its transpose.

Eg. Lets take a 2 $\times$ 2 matrix $\left[\begin{array}{cc}1& 2\\ 2& 2\end{array}\right]$

If we take its transpose the transpose matrix will be $\left[\begin{array}{cc}1& 2\\ 2& 2\end{array}\right]$ which is equal to the original matrix itself. So these type of matrices which remain same after taking the transpose are called as symmetric matrices.