Find Matrix A

Given:

\[ A + \begin{bmatrix} 2 & 3 \\ -1 & 4 \end{bmatrix} = \begin{bmatrix} 3 & -6 \\ -3 & 8 \end{bmatrix} \]

Step 1: Use Matrix Subtraction

\[ A = \begin{bmatrix} 3 & -6 \\ -3 & 8 \end{bmatrix} – \begin{bmatrix} 2 & 3 \\ -1 & 4 \end{bmatrix} \]

Step 2: Subtract Corresponding Elements

\[ A = \begin{bmatrix} 3 – 2 & -6 – 3 \\ -3 – (-1) & 8 – 4 \end{bmatrix} \]

\[ A = \begin{bmatrix} 1 & -9 \\ -2 & 4 \end{bmatrix} \]

Final Answer:

\[ A = \begin{bmatrix} 1 & -9 \\ -2 & 4 \end{bmatrix} \]