Let M {\displaystyle {}M} be an n × n {\displaystyle {}n\times n} -matrix such that there exist n × n {\displaystyle {}n\times n} -matrices A , B {\displaystyle {}A,B} satisfying M ∘ A = E n {\displaystyle {}M\circ A=E_{n}} and B ∘ M = E n {\displaystyle {}B\circ M=E_{n}} . Show that A = B {\displaystyle {}A=B} holds, and that M {\displaystyle {}M} is invertible.
