This is an upper triangular matrix, therefore its eigen values or characteristic roots will be the diagonal elements $(1, -1, i, -i)$
therefore, $(\lambda - 1)(\lambda + 1)(\lambda - i)(\lambda + i) = 0$ will hold true
which will give the characteristic equation as:
$\lambda ^{4} - 1 = 0$
and according to Cayley Hamilton theorem every matrix satisfies its own characteristic equation
$\Rightarrow A^{4} - I = 0$
$\Rightarrow A^{4} = I$