Question

If for a matrix $A,A+I=O$, where $I$ is an identity matrix, then $A$ equals

• A. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
• B. $\left[\begin{array}{cc}-2& 0\\ 0& -2\end{array}\right]$
• C. $\left[\begin{array}{cc}1& 2\\ -1& 1\end{array}\right]$
• D. $\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$

Answer 1

The correct option is D $\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$

We have,
$A+I=O$
$\Rightarrow A=O-I$
$\Rightarrow A=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]-\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
$=\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$
Option $D$ is correct.