I came across the following problem that says:
For $n >1$,let $\displaystyle f(n)$ be the number of $n \times n$ real matrices $A$ such that $A^2+I=0.$ Then which of the following options is correct?
$1.\displaystyle f(n) \equiv 0$
$2.\displaystyle f(n) \equiv \infty$
$3.\displaystyle f(n)=0$ iff $n$ is even
$4.\displaystyle f(n)=0$ iff $n$ is odd.
Can someone throw light on it? Thanks in advance for your time.