Calculate the determinant of a matrix multiplied by itself confirmation If $ \det B = 4$ is then is $ \det(B^{10}) = 4^{10}$?
Does that also mean that $\det(B^{-2}) = \frac{1}{\det(B)^2} $
Or do I have this completely wrong?

$det(B^2)$ means $ det(B*B)$ means at first, By multiplying two matrices you are getting a matrix and then you are finding determinant of that matrix
Similarly, $det(B^{10})$ means at first you are multiplying 10 matrices , that will give you a matrix and then finding the determinant
But in the case of the negative power only $B^{-m} $where m is a positive number
it is defined with respect to $B^{-1}$ that is $(B^{-1})^m$
hence, if $B^{-1}$ is defined then we can define $B^{-m}$
Here $det(B)\neq  0 $  therefor B is not singular hence $B^{-1}$ exists
So it has the menaing  
