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Matrices — Maths STD 12 Science — Question

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

Answer

Given that $A^2=A$
\[\begin{array}{l}
\text { Consider }(I+A)^2-3 A=I^2+A^2+2 A I-3 A \\
=I+A+2 A-3 A \quad\left[\because I^2=I, A^2=A \text { (given) }\right] \\
=1 \\
\end{array}\]

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