A = $\begin{bmatrix$}[r] x & 0 \ 1 & 1 \end{bmatrix}, B = \begin{bmatrix}[r] 4 & 0 \ y & 1 \end{bmatrix}\text{ and } C = \begin{bmatrix}[r] 4 & 0 \ x & 1 \end{bmatrix}.

Find the values of x and y, if AB = C.

$\phantom{\Rightarrow} AB = C \\[1em] \Rightarrow \begin{bmatrix$}[r] x & 0 \ 1 & 1 \end{bmatrix}\begin{bmatrix}[r] 4 & 0 \ y & 1 \end{bmatrix} = \begin{bmatrix}[r] 4 & 0 \ x & 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] x \times 4 + 0 \times y & x \times 0 + 0 \times 1 \ 1 \times 4 + 1 \times y & 1 \times 0 + 1 \times 1 \end{bmatrix} = \begin{bmatrix}[r] 4 & 0 \ x & 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 4x + 0 & 0 + 0 \ 4 + y & 0 + 1 \end{bmatrix} = \begin{bmatrix}[r] 4 & 0 \ x & 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 4x & 0 \ 4 + y & 1 \end{bmatrix} = \begin{bmatrix}[r] 4 & 0 \ x & 1 \end{bmatrix} \\[1em] \Rightarrow 4x = 4 \text{ and } 4 + y = x \\[1em] \Rightarrow x = \dfrac{4}{4} \text{ and } 4 + y = x \\[1em] \Rightarrow x = 1 \text{ and } 4 + y = 1 \\[1em] \Rightarrow x = 1 \text{ and } y = 1 - 4 = -3.

Hence, x = 1 and y = -3.