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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices2 Marks
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 $BA = C^2.$ Find the values of $p$ and $q.$
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Answer

$ 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] $
$ BA =\left[\begin{array}{cc}0 & -q \\ 1 & 0\end{array}\right]\left[\begin{array}{cc}p & 0 \\ 0 & 2\end{array}\right]=\left[\begin{array}{cc}0 & -2 q \\ p & 0\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]$
$BA = C^2$
$\Rightarrow -2q = -8$
$\Rightarrow q = 4$
$p = 8$
$\Rightarrow p = 8.$

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