Question

$A=\left[\begin{array}{cc}-2& 4\\ -1& 2\end{array}\right]$, then $A^2$ is equal to

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

Answer 1

Answer: (A)

Null matrix

$A=\left[\begin{array}{cc}-2& 4\\ -1& 2\end{array}\right]$

$A.A.=A^2=\left[\begin{array}{cc}-2& 4\\ -1& 2\end{array}\right]\left[\begin{array}{cc}-2& 4\\ -1& 2\end{array}\right]=\left[\begin{array}{c}4-4-2\times 4+4\times 2\\ -1x-2+2x-1-1\times 4+2\times 2\end{array}\right]$

$A^2=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]=O=$ null matrix.