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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 $A^2=1$, then $(A-1)^3+(A+1)^3-7 A$ is equal to :
  • ✓
    $A$
  • B
    $I - A$
  • C
    $I + A$
  • D
    $3A$
✓

Answer

Correct option: A.
$A$
$(A-I)^3+(A+I)^3-7 A$
$=A^3-I^3-3 A^2 I+3 A I^2+A^3+I^3+3 A^2 I+3 A I^2-7 A$
$=2 A^3+6 A I^2-7 A$
$=2 A \cdot A^2+6 A-7 A$
$=2 A \cdot I-A\left(\because A^2=1\right)$
$=2 A-A$
$=A$
Hence, the correct option is $(a).$

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