Question: How would you prove it?

Hello everybody!

Im working on my great great (not great at all.. ) Dutch math book. Im really considering getting a copy of "Advanced Engineering Mathematics, by Robert Lopez". But hey, i worked through the first book, and now im at the half of the other second book. So i will finish it.

They left me with no clue on how to get the deal done, that is what is so perfect about this book i guess (i did a lot of books, but these Dutch books, yeah they do me like that) they will leave you in the dark, while they get all the grandeur because they know how to get it done, and you as the reader, well as a first timer, dont know how. Ive talked to a lot of students about this book. Yes it sucks. Classes full of students did agree on that, the majority did. So yeah, im trying to get a book delivered from the university library to a university libary closer to me, so i can get the book that does have good reviews.

The things i did learn from the Dutch math book did work great in statics and mechanics. That made short work of all the questions like a hot knife through butter.

THE ACTUAL QUESTION:
I cant prove this, because i dont know how. The translation says: a. Prove that the inverse of A exists for all values of p.

b. Determine the inverse of A

My take on it thusfar:

Thank you!

Greetings,

The Function

Download Mapleprimes_Question_Book_2_Paragraph_4.4_Question_9a.mw