Let λ be eighen value
Characteristic polynomial is
$(1-λ)(-1-λ)(i-λ)(-i-λ)$
$=\left ( \lambda ^{2}-1 \right )\left ( \lambda ^{2}+1 \right )$
$=\lambda ^{4}-1$
Characteristic equation is $\lambda ^{4}-1=0$
According to Cayley Hamilton theorem every matrix matrix satisfies its own characteristic equation
So, $A^{4}=$$I$