Q54 of 307 Page 5

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

Given.

We need to prove that P(x)P(y) = P(x + y) = P(y)P(x).

First, we will evaluate P(x)P(y).

Now, we will evaluate P(y)P(x).

Thus, P(x)P(y) = P(x + y) = P(y)P(x).

If then verify that A² + A = (A + I), where I is the identity matrix.

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

If and prove that

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