For a lossless channel matrix, how to prove no source information is lost in transmission?

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For example: If the Channel matrix for Lossless Channel is $$P(Y\mid X) = \begin{bmatrix} 0.5 & 0.5 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0.25 & 0.25 & 0.5 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix},$$ then how can we prove no source information is lost in transmission?