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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices1 Mark
MCQ
If matrix $\text{A}=\big[\text{a}_{\text{ij}}\big]_{2\times2}$ where $\text{a}_\text{ij}=\begin{cases}1,&\text{if }\text{i }\neq\text{j}\\0,&\text{if }\text{i }=\text{j}\end{cases},$ then $A^2$ is equal to:
  • ✓
    $I$
  • B
    $A$
  • C
    $O$
  • D
    $-I$
✓

Answer

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

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