A square matrix A is called nilpotent if Ak = 0 for some k 0. Prove that if A is
nilpotent, then I + A is invertible.

Question

A square matrix A is called nilpotent if Ak = 0 for some k > 0. Prove that if A is
nilpotent, then I + A is invertible.

myininaya · Answer

hey i think i seen this question b4
let me see something

myininaya · Answer

my book's definition is different

myininaya · Answer

they say a square matrix A is said to be nilpotent if A^r=0 for some integer r>=1

myininaya · Answer

ryan its been awhile since i taken this course
do you think the definitions are the same?

myininaya · Answer

well they seem to be different to me

myininaya · Answer

If A is nilpotent, then we have Ak=0 for some k>0.
If Ak=0, then doesn't mean A=0.
if A=0, then I+A=I.
I is invertible since it is the identity matrix.
this sounds good to me lol