Explain why the following two problems are in $P.$ Your explanation does not need to be a formal proof but should be clear enough to explain how the process runs in polynomial time and under what conditions YES and NO are output.

$($a$)$ Given an $nn$ matrix of integers, is there a contiguous submatrix $($not necessarily square$)$ which sums to $0?$ Assume addition of any two integers is $(1).$

Solution:

$($b$)$ Given a simple, connected, unweighted, undirected graph with $n3$ vertices represented by an adjacency matrix $A,$ is there a cycle of length exactly $3?$

Solution: