Question
Find the value of $x$ given that $A=\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right] , B=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right]$
✓
Answer
$\begin{array}{l} A =\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right] \end{array} $
$ \therefore A ^2=\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right] $
$ =\left[\begin{array}{cc}4 & 36 \\ 0 & 1\end{array}\right] $
$ \because A ^2= B ($given$)$
$ \therefore\left[\begin{array}{cc}4 & 36 \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right] $
$ \therefore x =36 .$
$ \therefore A ^2=\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}2 & 12 \\ 0 & 1\end{array}\right] $
$ =\left[\begin{array}{cc}4 & 36 \\ 0 & 1\end{array}\right] $
$ \because A ^2= B ($given$)$
$ \therefore\left[\begin{array}{cc}4 & 36 \\ 0 & 1\end{array}\right]=\left[\begin{array}{ll}4 & x \\ 0 & 1\end{array}\right] $
$ \therefore x =36 .$
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