Question

Given $A=\left[\begin{array}{cc}1& -1\\ 2& -1\end{array}\right]$, which of the following result is true?

• A. $A^2=I$
• B. $A^2=-I$
• C. $A^2=2I$
• D. None of these

Answer 1

Answer: (B)

$A^2=-I$

Given, $A=\left[\begin{array}{cc}1& -1\\ 2& -1\end{array}\right]$
Now, $A^2=\left[\begin{array}{cc}1& -1\\ 2& -1\end{array}\right]\left[\begin{array}{cc}1& -1\\ 2& -1\end{array}\right]$
$=\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$
$\Rightarrow A^2=-I$