1. The problem asks to find $A^2$ for the matrix $A = \begin{pmatrix} x & 0 \\ 5 & y \end{pmatrix}$. 2. To find $A^2$, we multiply matrix $A$ by itself: $$A^2 = A \times A = \begin{pmatrix} x & 0 \\ 5 & y \end{pmatrix} \times \begin{pmatrix} x & 0 \\ 5 & y \end{pmatrix}.$$ 3. Perform the matrix multiplication step-by-step: - The element at position (1,1) is $x \cdot x + 0 \cdot 5 = x^2 + 0 = x^2$. - The element at position (1,2) is $x \cdot 0 + 0 \cdot y = 0 + 0 = 0$. - The element at position (2,1) is $5 \cdot x + y \cdot 5 = 5x + 5y$. - The element at position (2,2) is $5 \cdot 0 + y \cdot y = 0 + y^2 = y^2$. 4. So, the resulting matrix is: $$A^2 = \begin{pmatrix} x^2 & 0 \\ 5x + 5y & y^2 \end{pmatrix}.$$