Question

Find the value of x, given that $A^2$ = B,

A= $\left[\begin{array}{cc}2& 12\\ 0& 1\end{array}\right],B=\left[\begin{array}{cc}4& x\\ 0& 1\end{array}\right]$
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Answer 1

$A^2=B$

$\left[\begin{array}{cc}2& 12\\ 0& 1\end{array}\right]\left[\begin{array}{cc}2& 12\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}4& x\\ 0& 1\end{array}\right]$

$\left[\begin{array}{cc}4+0& 24+12\\ 0+0& 0+1\end{array}\right]=\left[\begin{array}{cc}4& x\\ 0& 1\end{array}\right]$

$\left[\begin{array}{cc}4& 36\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}4& x\\ 0& 1\end{array}\right]$

Therefore x = 36