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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$, then $A^2$ is equal to
  • A
    $\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$
  • B
    $\left[\begin{array}{ll}4 & 0 \\ 4 & 0\end{array}\right]$
  • C
    $\left[\begin{array}{ll}0 & 2 \\ 0 & 4\end{array}\right]$
  • ✓
    $\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right]$
✓

Answer

Correct option: D.
$\left[\begin{array}{ll}4 & 0 \\ 0 & 4\end{array}\right]$
(d) : We have, $A=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$
$
\Rightarrow \quad A^2=\left[\begin{array}{ll}
0 & 2 \\
2 & 0
\end{array}\right]\left[\begin{array}{ll}
0 & 2 \\
2 & 0
\end{array}\right]=\left[\begin{array}{ll}
0+4 & 0+0 \\
0+0 & 4+0
\end{array}\right]=\left[\begin{array}{ll}
4 & 0 \\
0 & 4
\end{array}\right]
$

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