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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
Choose the correct answer from the given four options. If $\text{A}=\begin{bmatrix}1&0\\0&1\end{bmatrix},$ then $A^2$ is equal to:
  • A
    $\begin{bmatrix}0&1\\1&0\end{bmatrix}$
  • B
    $\begin{bmatrix}1&0\\1&0\end{bmatrix}$
  • C
    $\begin{bmatrix}0&1\\0&1\end{bmatrix}$
  • ✓
    $\begin{bmatrix}1&0\\0&1\end{bmatrix}$
✓

Answer

Correct option: D.
$\begin{bmatrix}1&0\\0&1\end{bmatrix}$
$\because\ \text{A}^2=\text{A}.\text{A}$
$=\begin{bmatrix}0&1\\1&0\end{bmatrix}.\begin{bmatrix}0&1\\1&0\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$

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