The correct answer is B. $(\det B)^{-1}$.
A square matrix is non-singular if its determinant is non-zero. The determinant of a matrix is a number that is associated with the matrix. It can be used to determine whether the matrix is invertible, and it can also be used to calculate the inverse of a matrix.
The determinant of a product of matrices is the product of the determinants of the matrices. So, if $B$ is a square matrix, then $\det(B^{-1}) = (\det B)^{-1}$.
Option A is incorrect because the determinant of a non-singular matrix is non-zero.
Option C is incorrect because the determinant of a matrix is a number, not a negative number.
Option D is incorrect because the determinant of a matrix is a number, not the matrix itself.