\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
If a Markov chain has a transition matrix \(\mathbf{M} = \begin{pmatrix} 1 & 0 \\ 0.5 & 0.5 \end{pmatrix}\), what is the value of \((\mathbf{M}^2)_{21}\)?