The tutor gives an example to show that with matrices, AB=AC doesn’t mean B=C.

Consider the matrices A, B, C, and D:

By matrix multiplication, AB=AC. (In fact, both products equal D.) Yet, obviously, B≠C. Matrix multiplication lacks the cancellation law that you see with the real numbers.

HTH:)

Source:

Johnson/Riess/Arnold. Introduction to Linear Algebra. Don Mills: Addison-Wesley, 1989.