Question
If $\left[\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right]$ find $a, b, c$ and $d$
✓
Answer
Given
$\begin{array}{l}{\left(\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right)\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)=\left(\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right)} \end{array} $
$ \Rightarrow\left(\begin{array}{cc}a+0 & -b+0 \\ 0+c & 0+d\end{array}\right)=\left(\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right) $
$ \Rightarrow\left(\begin{array}{cc}-a & -b \\ c & d\end{array}\right)=\left(\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right)$
Comparing the corresponding elements
$–a = 1$
$\Rightarrow a = –1$
$–b = 0$
$\Rightarrow b = 0$
$c = 0$ and $d = –1$
Hence $a = –1, b = 0, c = 0, d = –1.$
$\begin{array}{l}{\left(\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right)\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)=\left(\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right)} \end{array} $
$ \Rightarrow\left(\begin{array}{cc}a+0 & -b+0 \\ 0+c & 0+d\end{array}\right)=\left(\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right) $
$ \Rightarrow\left(\begin{array}{cc}-a & -b \\ c & d\end{array}\right)=\left(\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right)$
Comparing the corresponding elements
$–a = 1$
$\Rightarrow a = –1$
$–b = 0$
$\Rightarrow b = 0$
$c = 0$ and $d = –1$
Hence $a = –1, b = 0, c = 0, d = –1.$
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