Suppose A=BC, where B is invertible. Show that any sequence of row operations that reduces B to I also reduces A to C. The converse is not true, since the zero matrix may be factored as 0 = B.0. Which of the following pieces of information in the problem statement are relevant for showing that any sequence of row operations that reduces B to I also reduces A to C?

A. The converse is not true.
B is invertible.
C. The zero matrix may be factored as 0 =B=0.
D. A= BC.