Suppose that A is a 5x5 matrix with determinant 5, and when you delete the second row and fourth column, the determinant of the resulting matrix is -15. If B=A^-1, which entries of B can we determine with certainty.
I know to use the cofactor formula on this problem, but not sure where to go from there.
If you delete the second row and fourth column, the determinant of the resulting object is the minor $M_{2,4}$. The cofactor $C_{2,4} = (-1)^{2+4} M_{2,4} = -15$.
The cofactor formula says that
$$ A^{-1} = \frac{1}{\det(A)} C^T $$
So this means that the entry $B_{4,2} = \frac{1}{5} C_{2,4} = -3$.