For the first question, the matrix B is just the adj(A)?
I have no idea where to begin with the second question, if anyone could help me get started.
Any help is greatly appreciated!
The easiest way to do it..
Given that A is an invertible, nxn matrix, we have that: $\displaystyle \det (A) = \sqrt[n-1]{\det \big[ \text{adj} (A) \big]}$
This can be derived from the relationship: $\displaystyle \det (A) A^{-1} = \text{adj} (A)$
where you take the determinant of both sides and solve.