Using Solve to solve my equation with Matrices

I’m attempting to solve an equation that involves matrices (so I suppose a system of equations). I have my matrices defined as follows:

Subscript[H, 1] = {{a, 0, 0}, {0, b, 0}, {0, 0, c}} Subscript[H, 0] = {{0, 0, 0}, {0, \[Omega], 0}, {0, 0, 2 \[Omega] + \[Alpha]}} Subscript[H, int] = \[CapitalOmega]/2 {{0, 1, 0}, {1, 0, Sqrt[2]}, {0, Sqrt[2], 0}} Subscript[G, 1] = {{Subscript[g, 11], Subscript[g, 12], Subscript[g, 13]}, {Subscript[g, 21], Subscript[g, 22], Subscript[g, 23]}, {Subscript[g, 31], Subscript[g, 32], Subscript[g, 33]}}  

And my function comm defined as follows:

comm[matrixone_, matrixtwo_] := matrixone . matrixtwo - matrixtwo . matrixone 

I’ve tried using the Solve function as follows:

Solve[Subscript[H, 1] ==    Subscript[H, int] +     I*comm[Subscript[G, 1], Subscript[H, 0]], {Subscript[g, 11],    Subscript[g, 12], Subscript[g, 13], Subscript[g, 21], Subscript[g,    22], Subscript[g, 23], Subscript[g, 31], Subscript[g, 32],    Subscript[g, 33]}] 

And it gives me a matrix with no elements. Any suggestions on how I can fix this would be appreciated as I’m basically brand new to mathematica.