Hi, I'm having trouble figuring this out:

A is an nxn matrix. It's given that A^{2}=A, A=\=0, A=\=I (I is nxn)

prove or disprove: Ax=0has only the trivial solution

I tried to disprove that with the determinant:

det(A^{2})=det(A)

2det(A)=det(A)

det(A)=0

Hence A is singular

BUT im not sure that thisdet(Ais right, and I can't fathom why^{2})=2det(A)A=\=0, A=\=I (I is nxn)is given, so I suspect I'm mistaken.

help is very welcomed