Question

If $A=\left[\begin{array}{cc}3& x\\ 0& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}9& 16\\ 0& -y\end{array}\right]$, $findxandywhen$ $A^2=B$.

• A. x = 4 and y = −1
• B. x = −4 and y = −1
• C. x = 4 and y = 1
• D. x = 4 and y = 2

Answer 1

The correct option is A

x = 4 and y = −1

$Given$, $A=\left[\begin{array}{cc}3& x\\ 0& 1\end{array}\right]andB=\left[\begin{array}{cc}9& 16\\ 0& -y\end{array}\right]$
Also, $A^2=B$
$\Rightarrow A.A=B$
$\Rightarrow \left[\begin{array}{cc}3& x\\ 0& 1\end{array}\right]\left[\begin{array}{cc}3& x\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}9& 16\\ 0& -y\end{array}\right]\Rightarrow \left[\begin{array}{cc}9& 4x\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}9& 16\\ 0& -y\end{array}\right]$
$Bycomparingthecorrespondingelements$
$\Rightarrow 4x=16$ and $1=-y$
$\Rightarrow x=4$ and $y=-1$