The coupling matrix in structural-acoustic systems carries the entire information about the coupled resonances. We have found an elegant way of presenting this matrix and computing its determinant analytically (in a closed-form) for light fluid loading cases. The determinant gets factorized into a product. This form can be used to gain an insight into the new order of the coupled resonances. The specific example of a rectangular panel backed by a cavity is taken to demonstrate the method. This being the primary objective of the work, secondarily, the form of the matrix so derived is used to compute the new coupled resonances using a simple iterative scheme requiring a starting guess. Numerical values are compared with those given in the literature and also using the commercial package virtual lab.