I'm learning about transition matrix and I'm sure about about the meaning of the element at ith row and jth column. The entry in ith row and jth column giving the probability that j is received when i is sent or in the opposite way?
Examples:
$[p(y|x)] = \begin{pmatrix}0.3&0.2&0.5\\0.5&0.3&0.2\\0.2&0.5&0.3\end{pmatrix}$
$[p(y|x)] = \begin{pmatrix}\frac13&\frac16&\frac12\\\frac13&\frac12&\frac16\end{pmatrix}.$
In general it is a matter of definition whether the rows or columns indicate the received symbol. However, it is common [1] that the columns corresponds to receive symbols and rows correspond to transmit symbols.
In your case, one can see from the second example that the columns correspond to the received symbol, since it needs to hold that $$ \sum_y p(y|x) = 1 $$ for all transmit symbols $x$.
[1] Ash, Robert B., Information theory., New York: Dover Publications, Inc. xi, 339 p. (1990). ZBL0768.94005.