Are all symmetric matrices ​invertible?

Is any symmetric matrix ​​invertible? I'm trying to prove this theoretical question, but I don't know what I need to do. I apologize for the simple question, but I'm in doubt and need clarification.

Solution 1:

It is incorrect, the $0$ matrix is symmetric but not invertable.

Solution 2:

Adding a couple of non zero example for future reference: $$\left[\begin{matrix} 1 & 1 \\ 1 & 1\end{matrix}\right]$$ is symmetric; but not invertible.

Also, $$\left[\begin{matrix} 2 & 2 & 1 \\ 2 & 2 & 1 \\ 1 & 1 & 1\end{matrix}\right]$$ $$\left[\begin{matrix} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1\end{matrix}\right]$$ and the list goes on. (they are all singular, that is, determinant is zero.)