Deterministic Channel is a #Discrete Memoryless Channel (DMC) that has only one non-zero element in each row which is shown below as Channel Matrix:
$$ P = \left[ \begin{array}{ccc} 1 & 0 & 0\\ 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{array} \right] $$
Noiseless Channel is a #Discrete Memoryless Channel (DMC) if it satisfies both characteristics of #Deterministic Channel and #Lossless Channel. It has only one non-zero element for each row and column, which also means that the sizes for both input alphabet and output alphabet are the same, i.e., \(j-1 = k-1\).