Question

If A and B are matrix. And if AB=AC can I say that B is equal the C?

Answer 1

Only if A is invertible.

Answer 2

I think... Can someone reaffirm my statement?

Answer 3

\[A^{-1} \cdot AB=A^{-1} \cdot AC => I B=I C => B=C \]
If A is invertible !

Answer 4

I got it now. Suppose A is the zero matrix. Then \(AB =AC\) and they're both the zero matrix, but B may not equal C. So it's not true.