Since D is invertible then D^(-1)exist and DD^(-1)=I_n. Here B and C are m * n matrices such that
-> (B-C)D * D^(-1)=0 * D^(-1)
We know that (B-C)D=0
Since D it invertible, D has an inverce D^(-1)
We multiply both sides of (B-C)D=0 by D^(-1) on the right side:
(B-C)D * D^(-1)=0 * D^(-1)
Note that 0D^(-1)=I_n, and 0D^(-1)}=0
So we are left with B-C=0, which rearranges to B=C
( B - C )D = 0 where B and C are m * n matrix and D is invertible.
Then, we have to prove that B = C.
Since, D is invertable so D^(-1) exist.
Now, from the given equation (B-C)D=0
Thus, we obtained our desired result.