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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
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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