Given A= [ ll p & 0 0 & 2 ], B= [ cc 0 & -q 1 & 0 ] C= [ cc 2 & -2 2 & 2 ] and B A=C^2 Find the values of p and q

B A= [ cc 0 & -q 1 & 0 ] [ ll p & 0 0 & 2 ]= [ cc 0 & -2 q p & 0 ] A= [ ll p & 0 0 & 2 ], B=p [ cc 0 & -q 1 & 0 ], C= [ cc 2 & -2 2 & 2 ] C^2= [ cc 2 & -2 2 & 2 ] [ cc 2 & -2 2 & 2 ]= [ cc 0 & -8 8 & 0 ] B A=C^2 [ cc 0 & -2 q p & 0 ]= [ cc 0 & -8 8 & 0 ] By comparing, -2a = -8 = > q = 4 And p = 8

Given A= [ ll p & 0 0 & 2 ], B= [ cc 0 & -q 1 & 0 ] C= [ cc 2 & -…

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Question

Given $A=\left[\begin{array}{ll}p & 0 \\ 0 & 2\end{array}\right], B=\left[\begin{array}{cc}0 & -q \\ 1 & 0\end{array}\right] C=\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right]$ and $B A=C^2$ Find the values of $p$ and $q$

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Answer

$B A=\left[\begin{array}{cc}0 & -q \\ 1 & 0\end{array}\right]\left[\begin{array}{ll}p & 0 \\ 0 & 2\end{array}\right]=\left[\begin{array}{cc}0 & -2 q \\ p & 0\end{array}\right]$
$A=\left[\begin{array}{ll}p & 0 \\ 0 & 2\end{array}\right], B=p\left[\begin{array}{cc}0 & -q \\ 1 & 0\end{array}\right], C=\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right]$
$C^2=\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right]\left[\begin{array}{cc}2 & -2 \\ 2 & 2\end{array}\right]=\left[\begin{array}{cc}0 & -8 \\ 8 & 0\end{array}\right] $
$ B A=C^2 \Rightarrow\left[\begin{array}{cc}0 & -2 q \\ p & 0\end{array}\right]=\left[\begin{array}{cc}0 & -8 \\ 8 & 0\end{array}\right]$
By comparing,
$-2a = -8 = > q = 4$
And $p = 8$