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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A$ is square matrix such that $A^2=A$, then $(I+A)^3-7 A$ is equal to
  • A
    $A$
  • B
    $1+ A$
  • C
    $1-A$
  • ✓
    $1$
✓

Answer

Correct option: D.
$1$
We have, $(I+A)^3-7 A$
$=I^3+A^3+3 I^2 A+3 I A^2-7 A=1+A \cdot A+3 A+3 A-7 A$
$=1+A+3 A+3 A-7 A=1$

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