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

Question

If A is a square matrix such that A2=I then (A-I)3+(A+I)3-7 A s equal to . (A) I+A (B) I-A (C) A (D) 3 A

Tardigrade Admin · Accepted Answer

(A-I)3+(A+I)3-7 A =A3-I-3 A2+3 A+A3+I+3 A2+3 A-7 A =2 A3-A =A(2 A2-I) =A(2 I-I)=A

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