1) What would a trivial lower bound be for the matrix multiplication of two n-by-n matrices?

2) What would an adversarial argument for the lower bound of finding the smallest element in an unsorted array containing n elements?

3) Suppose that a problem of type Q can be reduced to a problem of type P in O(n) time. After we solve the problem of type P, we can extract the answer to the original problem of type Q in O(n2) time. If we know that a problem of type Q has a know lower bound of (n5), then what can we conclude about the lower bound for a problem of type P?