Given matrix A = $\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$, we need to find 8A^–4. For a 2x2 matrix, A satisfies its characteristic equation: A² - (trace)A + (det)I = 0. Here, trace = 5, det = -2, so A² = 5A + 2I. Higher powers can be expressed as linear combinations of A and I. We find A^–1 = (1/-2)(A - 5I) = $\left[\begin{array}{cc}-2& 1\\ 1.5& -0.5\end{array}\right]$. Using the relation, we compute 8A^–4 and find it simplifies to 145A^–1 + 27I.

Final Answer: 145A^–1 + 27I