Question

If A = $\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]andB=\left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$, then value of $\alpha$ for which $A^2$ = B, is

• A. 1
• B. -1
• C. 4
• D. non real values

Answer 1

The correct option is D non real values

Given, $A=\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right],B=\left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$
$\Rightarrow A^2=\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]=\left[\begin{array}{cc}{\alpha }^2& 0\\ \alpha +1& 1\end{array}\right]$
Also, given. $A^2$ = B
$\Rightarrow \left[\begin{array}{cc}{\alpha }^2& 0\\ \alpha +1& 1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$
$\Rightarrow {\alpha }^2$ =1 and $\alpha$ + 1 = 5
Which is not possible at the same time.
$\therefore$ No real values of $\alpha$ exists.