Let A {\displaystyle A} be an m × m {\displaystyle m\times m} invertible matrix. Moreover let B {\displaystyle B} and C {\displaystyle C} be n × m {\displaystyle n\times m} matrices that satisfy ( B − C ) A = 0. {\displaystyle (B-C)A=0.} Show that B = C . {\displaystyle B=C.}
