Phineas is flipping a fair coin repeatedly and marking down the results. However, he has a soft spot for heads, so half the time he marks heads, he marks heads again. (This means he could possibly mark down heads many times in a row without actually flipping the coin again.) The resulting sequence of states could be modeled by a Markov chain, where the first possible state (and row of the matrix) is heads and the second possible state is tails. What is its transition matrix?

(A): $\begin{pmatrix} \tfrac{1}{2} & \tfrac{1}{2} \\ \tfrac{1}{2} & \tfrac{1}{2} \end{pmatrix}$

(B): $\begin{pmatrix} \tfrac{1}{2} & \tfrac{1}{2} \\ \tfrac{1}{4} & \tfrac{3}{4} \end{pmatrix}$

(C): $\begin{pmatrix} \tfrac{3}{4} & \tfrac{1}{2} \\ \tfrac{1}{4} & \tfrac{1}{2} \end{pmatrix}$

(D): $\begin{pmatrix} \tfrac{3}{4} & \tfrac{1}{4} \\ \tfrac{1}{2} & \tfrac{1}{2} \end{pmatrix}$