Matrix ƙungiyoyi sun ƙunshi matrices tare da matrix multiplication. The general linear group GL ((n, R) ya ƙunshi dukkan invertible n-by-n matrices tare da ainihin shigarwar. Ana kiran ƙananan ƙungiyoyinsa matrix ƙungiyoyi ko ƙungiyoyin layi. Misali na ƙungiyar dihedral da aka ambata a sama za a iya kallon su a matsayin (ƙaramin) matrix ƙungiya. Wani muhimmin matrix ƙungiya shine ƙungiyar orthogonal na musamman SOn (n). Yana bayyana duk yiwuwar juyawa a cikin n girma. Ta hanyar kusurwoyin Euler, ana amfani da matrix juyawa a cikin zane-zane na kwamfuta. Ka'idar wakilci ita ce aikace-aikacen ƙungiyar kuma yana da mahimmanci don zurfin fahimtar ƙungiyoyi. Yana nazarin ƙungiyar ta hanyar ayyukanta a kan wasu wurare.
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