Question:
If $A=\left[\begin{array}{ll}i & 0 \\ 0 & i\end{array}\right]$, write $A^{2}$
Solution:
Given : $A=\left[\begin{array}{ll}i & 0 \\ 0 & i\end{array}\right]$
$A^{2}=A A$
$\Rightarrow A^{2}=\left[\begin{array}{ll}i & 0 \\ 0 & i\end{array}\right]\left[\begin{array}{ll}i & 0 \\ 0 & i\end{array}\right]$
$\Rightarrow A^{2}=\left[\begin{array}{ll}i^{2}+0 & 0+0 \\ 0+0 & 0+i^{2}\end{array}\right]$
$\Rightarrow A^{2}=\left[\begin{array}{cc}i^{2} & 0 \\ 0 & i^{2}\end{array}\right]$
$\Rightarrow A^{2}=\left[\begin{array}{cc}-1 & 0 \\ 0 & -1\end{array}\right]$ $\left(\because i^{2}=-1\right)$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.