Question

If A = $\left[\begin{array}{ccc}i&0\\0&i\end{array}\right]$ find A².

Answer 1

Answer:

$A^{2}=-I$

Step-by-step explanation:

If  

$A=\left[\begin{array}{ccc}i&0\\0&i\end{array}\right]$  and  

So, to find  A²

$A^{2}=A\times A=\left[\begin{array}{ccc}i&0\\0&i\end{array}\right]\times \left[\begin{array}{ccc}i&0\\0&i\end{array}\right]$

$A^{2}=\left[\begin{array}{ccc}i^{2}&0\\0&i^{2}\end{array}\right]$

as we know that i² = -1

So

$A^{2}=\left[\begin{array}{ccc}-1&0\\0&-1\end{array}\right]$

or

$A^{2}=-1\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]\\\\=> A^{2}=-I$