1) How do you find A (by hand) if an adjoint of A 4 by 4 matrix is given you?

For example:

Adj A equals

2 0 0 0

0 2 1 0

0 4 3 2

0 -2 -1 2

what is A?

I know that A (adj. A) = (det. A) I

and I tried to find A by finding the Adj. A of the given Adj. of A and I got the weird numbers.

The answer is suposed to give the following matrix:

A equals

1 0 0 0

0 4 -1 1

0 -6 2 -2

0 1 0 1

How do you get to that? I had asked this several days ago and the links I received sort of helped but I got confused again. I tried to solve this twice and its frustrating that I am not getting the answer. Please if anyone could explain this with baby steps I don't mind at all I just want is to understand it. Thanks

2) Let R denote the set of real numbers. Define scalar multiplication by

a x= a *x (the usual multiplication of real numbers)

and define the addition, denoted Å , by

x Å y = max (x, y) (the maximum of the two numbers)

Is R a vector space with these operations? Prove your answer.

( I have no idea how to solve this one either)