If A= [ ll -2 & 4 -1 & 2 ], then A^2 is - Vidyadip

MCQ

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

✓
a null matrix
B
a unit matrix
C
equal to $\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right]$
D
equal to $\left[\begin{array}{ll}0 & 0 \\ 0 & 1\end{array}\right]$

✓

Answer

Correct option: A.

a null matrix

(a) : Given that, $A=\left[\begin{array}{ll}-2 & 4 \\ -1 & 2\end{array}\right]$
$\therefore \quad A^2=\left[\begin{array}{ll}-2 & 4 \\ -1 & 2\end{array}\right]\left[\begin{array}{ll}-2 & 4 \\ -1 & 2\end{array}\right]=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
$\Rightarrow A^2$ is a null matrix.

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