If this is the correct man, I do have to question the dates that you list. A man who was 49 years old in 1861 was not very likely to enlist in the army. (Not impossible, but rare.) Also, the 1860 census of Floyd County, Georgia lists a George W. Mathis, aged 19, in the family of William and Anna Mathis. This is much more likely the man we see serving in the 21st Georgia Inf. and 6th Georgia Cav.