Can't get "collect" to extract the determinant of the inverse of a symbolic matrix.

I often invert complex symbolic matrices and end up with an impossibly complex result because matlab divides each term in the inverse by the determinant of the matrix. I'd like to extract the determinant as a common factor, but collect doesn't seem to work. For example, consider

syms a b c d
myMatrix = [a,b;c,d];
myInv    = inv(myMatrix);
simple(myInv)

This returns

[  d/(a*d - b*c), -b/(a*d - b*c)]
[ -c/(a*d - b*c),  a/(a*d - b*c)]

None of the commands invoked by "simple" do anything to the matrix. I'd like to find something that would return:

    [ d,-b;-c,a]/(a*d-b*c)

Answer 1

[Azzi Abdelmalek]

 myInv/det(myInv)

[Leo Simon]

Wow, that was easy, thanks! Actually for my purposes, I think

inv(myMatrix/det(myMatrix))

is what I want, so that for a complex matrix expression I don't have to generate the nasty myInv and then get rid of the determinant.