Problem involving the adjugate

[wakko101]

The question I'm dealing with is this:

Suppose adj(A) =
-1 2 -4
0 -3 0
0 0 3
Find A

I was trying to figure it out backwards, by using a 3x3 matrix of variables and doing the cofactor expansion thing and then seeing if I could figure out the values of the variables, but I'm not sure that's the way to go. I suspect there is a formula or theorem out there that will help me, but I can't figure out what it is.

Any help?

 

[matness]

Is the determinant of A given?
If it is so you can use A*adj(A)=det(A) *identity matrix
But if it is not i don't know what to do