Proving determinant property for arbitrary matrices

[Snowdeity]

Homework Statement

1) If A is a product of elementary matrices, show that det(adj(A))=(det(A))^(n-1)
2) Prove the above statement without the assumption on A

Homework Equations

Hmm... Know A*adj(A)=det(A)*In (i.e. the n by n identity matrix)

The Attempt at a Solution

Well I know the assumption implies the use of the equivalent theorems for invertible matrices...not sure how to set this up though. Have to show A as a n by n matrix in order to thoroughly prove it, but seems to get complicated quickly if trying to evaluate the adj(A)...
Anyone clue me in on this?

 

[kurt.physics]

2) Prove the above statement without the assumption on AWell, I guess in this case we should consider A as an arbitrary matrix (not necessarily a product of elementary matrices). So far I have started with A*adj(A)=det(A)*In. But not sure where to go from here...