The maximum value of $\det(A)$ where $A$ is a $4\times 4$ matrix made by the elements $-1$ and $1$ only is
(A) 8 $\qquad$ (B) 16 $\qquad$(C) 32 $\qquad$ (D) 28
My Attempt
For a $1\times 1$ determinant it is obviously 1
For a $2\times 2$ determinant it is $ad-bc$. Substituting $1$ and $-1$ we can see that maximum value is $2$.
Can some generalization be made?