If A is a square matrix and I is an identity matrix such that A^2=A, then A(I-2 A)^3+2 A^3 is equal to : Option 1: I+A Option 2: I+2 ~A Option 3: I-A Option 4: A

The answer is 'A'. View full solution:

Algebra > Matrices & Determinants

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If $A$ is a square matrix and $I$ is an identity matrix such that $A^{2}=A$, then $A(I-2 A)^{3}+2 A^{3}$ is equal to :

$\mathrm{I}+\mathrm{A}$

$\mathrm{I}+2 \mathrm{~A}$

$\mathrm{I}-\mathrm{A}$

$\mathrm{A}$

✅ Correct Option: 4

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If $A$ is a square matrix and $I$ is an identity matrix such that $A^{2}=A$, then $A(I-2 A)^{3}+2 A^{3}$ is equal to :

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