Determine the power of a matrix using technology with matrix arithmetic capabilities when appropriate.

Using technology with matrix arithmetic capabilities, determine \( M^4 \) for the matrix shown in the diagram.

A population transition matrix is given by \(M = \begin{pmatrix} 0.6 & 0.2 \\ 0.4 & 0.8 \end{pmatrix}\). This matrix describes how a population in two regions changes each year. Determine \(M^3\) to find the three-year transition matrix. Show your working and express your answer as a 2 × 2 matrix with entries correct to 2 decimal places.