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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A$ is a square matrix such that $A ^2= A,$ then $(I-A)^3+ A$ is equal to:
  • ✓
    $I$
  • B
    $0$
  • C
    $I - A$
  • D
    $I + A$
✓

Answer

Correct option: A.
$I$
$A^2=A$
$(I+A)^3+A$
$\Rightarrow 1^3-A^3-3 I^2 A+31 A^2+A$
$\Rightarrow 1-A^3-3 A+3 A+A\left( \therefore  A^2=A\right)$
$\Rightarrow 1-A \cdot A^2+A$
$\Rightarrow 1-A \cdot A+A$
$\Rightarrow 1-A+A$
$=1$

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