Question

$A=\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right],$ $B=\left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$ and $A^2=B,$ then

• A. $\alpha =-1$
• B. $\alpha =1$
• C. $\alpha =4$
• D. None of these

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\alpha =-1$
B $\alpha =1$
C $\alpha =4$

Given, $A^2=B$

$\Rightarrow {\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]}^2=\left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}{\alpha }^2& 0\\ \alpha +1& 1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$

By comparing above matrices, we get

${\alpha }^2=1$ and $\alpha +1=5$

$\Rightarrow \alpha =1$ or $\alpha =-1$ and $\alpha =4$