1. **Problem:** Given matrices $ A = \begin{bmatrix}4 & -6 \\ -2 & 3\end{bmatrix} $, $ B = \begin{bmatrix}7 & -8 \\ -4 & 5\end{bmatrix} $, and a 2x2 matrix $ X $, if $ AX = AB $, is $ X = B $? 2. **Formula and rules:** The equation $ AX = AB $ implies $ A(X - B) = 0 $. 3. **Intermediate work:** Since $ A $ is a matrix, if $ A $ is invertible, then multiplying both sides by $ A^{-1} $ gives: $$ A^{-1}A(X - B) = A^{-1}0 \Rightarrow \cancel{A^{-1}A}(X - B) = 0 \Rightarrow X - B = 0 $$ 4. **Conclusion:** Therefore, if $ A $ is invertible, $ X = B $. 5. **Check invertibility of $ A $:** Calculate determinant: $$ \det(A) = 4 \times 3 - (-6) \times (-2) = 12 - 12 = 0 $$ Since $ \det(A) = 0 $, $ A $ is not invertible. 6. **Implication:** Because $ A $ is not invertible, we cannot conclude $ X = B $ from $ AX = AB $. **Final answer:** $ \boxed{\text{No, } X \neq B \text{ necessarily because } A \text{ is not invertible.}} $