# How to derive transition matrix in this stochastic process?

I am new to stochastic processes and trying to solve a question related to finding a transition matrix of some experiment. The question is a

A sequence of experiments is performed, in each of which two fair coins are tossed. Let S1 indicate that two heads come up, S2 that a head and a tail come up. and S3 that two tails turn up. Find the transition matrix.

What I think is it is: $$\left(\matrix{1/4 & 1/4 & 0 \\ 0 & 1/2 & 1/4 \\0 & 1/2 & 1/2}\right)$$, but the sum of each row in transition matrix should be one. So my answer is not correct. Does anybody know how I can find these probabilities. Any help would be appreciated.

Given a stochastic process $$\{X_n\}_{n \in \mathbb{N}}$$ as described, see that each $$X_i$$ and $$X_j$$ are independent of each other, if $$i \neq j$$.
$$\begin{bmatrix} 1/4 & 1/2 & 1/4\\ 1/4 & 1/2 & 1/4\\ 1/4 & 1/2 & 1/4\end{bmatrix}$$
$$P(X_{i+1} = S_3|X_i= S_1) = 0.$$