Convergence of a Markov Process
R, &nbsp;44&nbsp; 43 bytes



function(m){X=m
while(any(X-(X=X%*%m)))0
X}


Try it online!

Just keeps multiplying until it finds a fixed matrix. Apparently X!=(X=X%*%m) does the comparison, then reassigns X, so that's neat.

Thanks to @Vlo for shaving off a byte; even though crossed out 44 is still regular 44.