Question

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

• A. $-1$
• B. $1$
• C. $4$
• D. no real values

Answer 1

The correct option is C $4$

Given, $A=\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$
$A^2=B$
$\Rightarrow \left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]\left[\begin{array}{cc}\alpha & 0\\ 1& 1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$
$\alpha +1=5$
$\therefore \alpha =4$