Question

Let $A=\left[\begin{array}{c}i0\\ 0i\end{array}\right]$, then find $A^4$. Where $i=\sqrt{-1}$.

Answer 1

Given,

$A=\left[\begin{array}{c}i0\\ 0i\end{array}\right]$.

Now, for a diagonal matrix $A$ we have,

$A^4$$=\left[\begin{array}{c}{i}^{4}0\\ 0i^4\end{array}\right]$

or, $A^4$$=\left[\begin{array}{c}10\\ 01\end{array}\right]$. [ Since $i^2=-1$ this gives $i^4=1$]