Question

Is a zero matrix symmetric?

Answer 1

Checking if a zero matrix is symmteric

A symmetric matrix is a square matrix that is equal to its transpose matrix i.e. $A^T=A.$

Considering a zero matrix: $\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$

The transpose of the zero matrix is: $\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$

We can see that the transpose of the zero matrix is a zero matrix itself.

Hence, a zero matrix is symmtric.