Cramer's rule and the chain rule are entirely unrelated.
The chain rule is a rule in calculus that lets you take the derivative of a composite function, such as h(x)=g(f(x)). It says that h'(x)=g'(f(x))*f'(x), or "outside derivative times inside derivative".
Cramer's rule is a method in linear algebra that allows you to solve a system of linear equations. It can be used to find the inverse of a matrix.
