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

.:

Option c is correct

We have $A^2 = A$

Now, ${(I + A)^3} - 7A = {I^3} + {A^3} + 3IA(I + A) - 7A$

$= I + {A^2} + 3A(I + A) - 7A = I + {A^2} + 3A + 3{A^2} - 7A$

$= I + 4{A^2} - 4A = I + 4A - 4A = I$