Show that if P and Q are two transition probability matrices with the same number of rows, and hence columns, then PQ is also a transition probability matrix. Note that this implies that if P is a...

Show that if P and Q are two transition probability matrices with the same number of rows, and hence columns, then PQ is also a transition probability matrix. Note that this implies that if P is a transition probability matrix, then so is Pⁿ
for any positive integer n.