# Non Linear Equation Solving with Matrices

Suppose I have the following matrix equalities:

A=X, B=Y

where the left-hand side matrices are numeric and the right hand side contains non-linear combinations of unknowns. Since I have quite a few variables, it would be tiresome to rewrite the equations one by one. Is there any clever way to solve the system implicitly defined above in Mathematica? Or do I have to grab each of the equations? Is there any quick way to explicitly write the equations?

Thanks.

A = {{1, 1}, {1, 1}};