Suppose A.B = A.C, what can you deduce about A, B and C?
If A.B = A.C, it means that the product of A and B is equal to the product of A and C. This implies that either A is the identity element (if it exists), or B = C. In other words, either A is a non-invertible element, or B and C are identical.
If A.B = A.C, it implies that A is a non-zero matrix, since otherwise the equation would not hold.
However, we cannot directly deduce much about B and C from this equation. It could mean that B and C are equal matrices, or it could mean that B and C represent different matrices that have the same effect on A when multiplied. To determine further information about B and C, we would need additional equations or information.