In this paper, we establish some necessary and sufficient conditions for the existence of solutions to the system of operator equations BXA = B = AXB in the setting of bounded linear operators on a Hilbert space, where the unknown operator X is called the inverse of A along B. After that, under some mild conditions we prove that an operator X is a solution of BXA = B = AXB if and only if B ∗≤ AXA, where the ∗-order C ∗≤ D means CC∗ = DC∗, C∗C = C∗D. Moreover we present the general solution of the above equation.

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