Determine whether or not the transformations an isomorphism, Then determine whether it has an inverse. If not, determine whether It has a left inverse. Justify your conclusion. а b+1 T: M2×2 R4 defined by T = cd 2b-3c d

Find the product of x2+3y and x23y.

Substract.simplify

Let P(R#) represent the set of all polynomial functions, functions that can be written in the form anxn + an-1xn-1 + ... + a1x + a0, for some integer n ≥ 0 and with an, an-1, ... a1 and a0 being real numbers, let the operation + represent polynomial addition, and let the operation * represent polynomial multiplication.a. Demonstrate or explain why the system (P(R#), +, *) is a ring, that is, demonstrate or explain why:i. (P(R#), +) is commutative groupii. (P(R#), *) is semi-groupiii. The operation * distributes over the operation +.