Let $A$ be a square matrix and $x$ be a vector whose dimensions match $A$. Let $B^{\dagger}$ be the conjugate transpose of $B$. Then which of the following is not true:
- $x^{\dagger} A^{2} x$ is always non-negative
- $x^{\dagger} A x$ could be zero
- $x^{\dagger} A x$ could be complex
- If $A=A^{\dagger}$ then $x^{\dagger} A x$ is real
- If $A=A^{\dagger}$ then $x^{\dagger} A y$ is complex for some vector $y$ with same dimensions as $x$