Question

if 3×3 matrix A has it inverse equal to A then A^2 ​

Answer 1

if A is a 3×3 matrix then it's inverse is equal to the same then it should be a diagonal matrix

example:

1 0 0

0 1 0 =A

0 0 1

then

A^2=A

proof:

1 0 0 1 0 0 1 0 0

0 1 0 × 0 1 0 =0 1 0

0 0 1 0 0 1 0 0 1

so from the above A^2=A

note: I didn't show the matrirx with symbol [ ] you should definitely put that symbols to above matrix