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MATRICES — MATHS STD 12 Science — Question

Rajasthan 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.
$I$
$A^2 = A$
$(I + A)^3 +A$
$\Rightarrow I^3 - A^3 - 3I^2A + 3IA^2 + A$
$\Rightarrow I - A^3 - 3A+ 3A + A \ [\therefore A^2 = A]$
$\Rightarrow I - A.A^2 + A$
$\Rightarrow I - A.A + A$
$\Rightarrow I - A + A$
$= I$

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