Question

If `A` is a square matrix such that `A^2=A ,` then `(I+A)^3-7A` is equal to
A. A
B. I-A
C. I
D. 3A

Answer 1

Correct Answer - A
`Given A^(2)=A`
`therefore (I+A)^(3)-7A=I^(3)+3I^(3)A +3IA^(2)+A^(3) -7A`
`=I+3A+3A^(2)+A^(3) -7A`
`=I+3A+3A +A.A^(2)-7A`
`=I-A+A.A`
`=I-A+A^(2)`
`=I-A+A=I`