is a square matrix such that =0. Prove that for any real number the matrix is invertible
Attempt: if =0 then is a singular matrix. A singular matrix times is still a singular matrix. so the idea is to prove that is an invertible matrix when A is singular.
I'm not sure where to go from here but this is something interesting I found:
C = D = C and D are both singular matrices.
1) C + = = invertible matrix
2) D + = = singluar matrix
So I believe the idea is to figure out why D is not part of the matrix we are looking for, even though it is singular, and it probably has to do with the fact that