If $A$ is real symmetric matrix

Question

If $A$ is real symmetric matrix then

a)does not contain $0$ eigenvalue

b)at least one eignvalue positive.

pick correct statement

1)option a is correct

2)option b is correct

3)both option a and b is correct

Answer 1

Consider $A_1=\begin{bmatrix}{1}&{0}\\{0}&{0}\end{bmatrix},\; A_2=\begin{bmatrix}{-1}&{0}\\{0}&{-1}\end{bmatrix}.$