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I want to define a group action in sage. The group is a direct product of two general linear groups. The set under action is of matrices and the action is $(A,B) (M)=A^{-1}BM$. Assume all matrices have compatible sizes in order for multiplication. I might need a stabelizer later so I was thinking doing it in GAP but could not figure out how. Any suggestions?

I want to define a group action in sage. The group is a direct product of two general linear groups. The set under action is of matrices and the action is $(A,B) (M)=A^{-1}BM$. (M)=A^{-1}MB$. Assume all matrices have compatible sizes in order for multiplication. I might need a stabelizer later so I was thinking doing it in GAP but could not figure out how. Any suggestions?