Q54 of 307 Page 5

If and prove that

Given and

We need to prove that.

First, we will evaluate PQ.

Now, we will evaluate QP.

Thus,

If then find A² – 5A – 14I. Hence, obtain A³.

If then show that P(x) P(y) = P(x + y) = P(y) P(x).

If find A² – 5A + 4I and hence find a matrix X such that A² – 5A + 4I + X = O.

If prove that for all positive integers n.