1. The problem is to find $A^2$, which means multiplying matrix $A$ by itself. 2. Suppose matrix $A$ is given by $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$. 3. To find $A^2$, calculate the product $A \times A$: $$A^2 = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \times \begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} a\cdot a + b\cdot c & a\cdot b + b\cdot d \\ c\cdot a + d\cdot c & c\cdot b + d\cdot d \end{bmatrix}$$ 4. Simplify each element: $$A^2 = \begin{bmatrix} a^2 + bc & ab + bd \\ ca + dc & cb + d^2 \end{bmatrix}$$ 5. This resulting matrix is $A^2$. If you provide the specific matrix $A$, I can compute $A^2$ explicitly for you.