Question

$(\begin{array}{cc}-1& 0\\ 0& 1\end{array})(\begin{array}{cc}a& b\\ c& d\end{array})=(\begin{array}{cc}1& 0\\ 0& -1\end{array})$, then the values of $a,b,c$ and $d$ respectively are

• A. $-1,0,0,-1$
• B. $1,0,0,1$
• C. $-1,0,1,0$
• D. $1,0,0,0$

Answer 1

The correct option is A $-1,0,0,-1$

$\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}-a& -b\\ c& d\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$

On comparing both sides, corresponding columns,

$\Rightarrow -a=1,$ $-b=0$ and $c=0$

$a=-1,$ $b=0$ and $d=-1$

Hence, the answer is $-1,0,0,-1.$