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In this paper, we show that both the general linear group $\gl{q}$ and thespecial linear group $\slg{q}$ have both the EKR property and the EKR-moduleproperty. This is done using an algebraic method; a weighted adjacency matrixfor the derangement graph for the group is found and Hoffman's ratio bound isapplied to this matrix. We also consider the group $\agl{q}$ and the2-intersecting sets in $\PGL(2,q)$.

Erd\H{o}s-Ko-Rado results for the general linear group, the special linear group and the affine general linear group