Finding the determinant of a matrix given the adjoint 
My attempt:
Knowing that $$A(AdjA) = IdetA$$
I took the determinant on both sides: $$det(A)det(AdjA) = det(det(A))$$
So, $$det(A)det(AdjA) = (det(A))^3$$
$$det(AdjA) = (det(A))^2$$
$$det(A) = (AdjA)^{0.5}$$
The adjoint was calculated to be 4
Thus, $$det(A) = 4^{0.5}=2$$
Why is the answer -2? 

Another way to is to using cofactor formula. We have 
$$\det(A)=a_{31}C_{31}+a_{32}C_{32}+a_{33}C_{33}
=C_{31}+2C_{32}+C_{33}.$$
From the adjoint of $A$, we know that 
$$C_{31}=-1, C_{32}=-1, C_{33}=1.$$
Therefore, we have 
$$\det(A)=C_{31}+2C_{32}+C_{33}=-1-2+1=-2.$$
