Question

If $A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$, then $A^2$ is equal to ______

• A. $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 0\\ 1& 0\end{array}\right]$
• C. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
• D. $\left[\begin{array}{cc}0& 1\\ 0& 1\end{array}\right]$

Answer 1

Answer: (C)

$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

We have, $A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$

Hence $A^2=AA=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$

$=\left[\begin{array}{cc}0\times 0+1\times 1& 0\times 1+1\times 0\\ 1\times 0+0\times 1& 1\times 1+0\times 0\end{array}\right]$

$=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$