If A3=0 , then I+A+A2 equals

Question

If A3=0 , then I+A+A2 equals (A) I-A (B) (I-A) (C) (I + A)- 1 (D) I

Tardigrade Admin · Accepted Answer

Consider I3-A3=(.I-A.)(.I2+IA+A2.)=(.I-A.)(.I+A+A2.) ⇒ I=(.I-A.)(.I+A+A2.) ⇒ (.I+A+A2.)=(. I - A .)- 1

Q. If $A^{3} = 0$ , then $I + A + A^{2}$ equals