L = lambda.
Prove: d(A^-1)/dL = -(A^-1)(dA/dL)(A^-1)
The Attempt at a Solution
I did this as an analogy with function of numbers, but don't know how to extend this to matricies. for example:
lets say A = f(L)
d(f(L)^-1)/dL = - (f(L)^-2*d(f(L))/dL = -(A^-1)*dA/dL*(A^-1)
But what is the matrix form?