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If A is a square matrix such that $A^{2} = I$ , then ${(A-I)}^{3} {+(A+I)}^{3} -7A$ is equal to

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Correct option is A

We have A2=I∴ (A-I)3+(A+I)3-7A=(A−I)+(A+I) (A−I)2+(A+I)2−(A−I)(A+I)−7A ∴ a3+b3 = (a+b)(a2+b2-ab) =(2A)2(A2+I2)-A2-I2-7A=2A2(I+I2)-A2+I2-7A ∵A2=I=2A[2(I+I)]-7A (I2=I)=8AI-7A=A

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If A is a square matrix such that A2= I, then (A-I)3+(A+I)3-7A is equal to

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If A is a square matrix such that $A^{2} = I$ , then ${(A-I)}^{3} {+(A+I)}^{3} -7A$ is equal to