I've been trying to solve this matrix equation but I just can't find the way to do it. The task is: Find matrix $\mathbf{X}$ from the equation in the photo where $\mathbf{A, B, C}$ are given matrices and $\mathbf{a}$ is a given number.
$$\mathbf{(AXB)^{-1}+aB^{-1}X^{-1}C=A^{-1}}$$
The problem is that I don't know how to manipulate with the equation in order to put $\mathbf{X}$ in one side side of the equation and the other matrices in the other side. If for example we have $\mathbf{AX=B}$ we multiply each side with $\mathbf{A^{-1}}$ on the left and we get $\mathbf{X=A^{-1}\cdot B}$
Can anyone help me!
Thank you!