KCET · Maths · Matrices
If \(A\) is a square matrix such that \(A^2=A\), then \((I-A)^3\) is
- A \(\mathrm{I}-\mathrm{A}\)
- B A - I
- C \(\mathrm{I}+\mathrm{A}\)
- D \(-\mathrm{I}-\mathrm{A}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{I}-\mathrm{A}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{A}^2=\mathrm{A}\).
\(\begin{aligned} & (I-A)^3=(I-A)\left(I-2 A+A^2\right) \\ & =(I-A)(I-2 A+A) \\ & =(I-A)(I+A) \\ & =I-A^2=I-A\end{aligned}\)
\(\begin{aligned} & (I-A)^3=(I-A)\left(I-2 A+A^2\right) \\ & =(I-A)(I-2 A+A) \\ & =(I-A)(I+A) \\ & =I-A^2=I-A\end{aligned}\)
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