What are the benefits finding the inverse of a matrix using the "adjoint" method over RREF?

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Good morning!

I am studying for a linear algebra test, where I know in advance that I will have to solve a system of equations (Ax = b) using Cramer's Rule and by also by multiplying A inverse with b.

Is there any situation in which it would be better to use the adjoint method to find the inverse?

I don't expect an answer before the test, but I got curious during my studies about the various applications of these rules.

Thanks!