 He was a co-founder and president of the Washington Library Company for thirteen years—the first public library in the District of Columbia—and was co-director and trustee of the District of Columbia Public Schools, where he was one of the superintendents of a school.Matthews was heavily involved in Catholic charitable organizations as well; he was the founder and president of St. Vincent's Female Orphan Asylum and the co-founder and president of St. Joseph's Male Orphan Asylum.He played a significant role in the founding of Washington Visitation Academy for girls, St. Peter's Church on Capitol Hill, and the parish that now includes the Cathedral of St. Matthew the Apostle.