Question

If $A=\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]$ and $B\left[\begin{array}{cc}1& 0\\ 3& 1\end{array}\right]$the value of $\alpha$ for which $A^2=B$ is

• A. 1
• B. -1
• C. $i$
• D. No real values of $\alpha$

Answer 1

Answer: (D)

We have $A^2\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]=\left[\begin{array}{cc}{\alpha }^2& 0\\ \alpha +1& 1\end{array}\right]$
As $A^2=B,$ we get ${\alpha }^2=1$ and $\alpha +1=3\Rightarrow \alpha =\pm 1$ and $\alpha =2.$ This is not possible.