Why is det(C)=det(A)^(n-1) for cofactors and determinants?

[Unusualskill]

Any1 can explain to me why det(C)=det(A)^(n-1)
where A is n-by-n matrix and C is the matrix of cofactors of A.
I have been thinking, any 1 can help?thx!

 

[Erland]

This follows from the equation AC=(det A)I, or equivalently A^-1= (1/det A)C (if det A≠0).