I was recently asked to find the right inverse of some matrixes. I found that all three of them were invertible, so it was just a matter of finding their inverses, which would be exactly the same as the right inverses.
What if a matrix is not invertible?
Basically, what I want to know is, if a matrix is not invertible, does it mean that there are no left and/or right inverses at all? That is,
$$|A| = 0 \iff \not \exists B(AB = I \ \lor \ BA = I)$$