t(tab)
did as it was asked, which was to pivot the object
tab <- matrix(c(10,3,3,1), nrow=2,ncol=2)
colnames(tab) <- c("No_Therapy","Therapy")
row.names(tab) <- c("No_Prozac","Prozac")
tab
#> No_Therapy Therapy
#> No_Prozac 10 3
#> Prozac 3 1
t(tab)
#> No_Prozac Prozac
#> No_Therapy 10 3
#> Therapy 3 1
which was, however, not what you wanted, which is to swap the positions of the columns and rows.
tab <- matrix(c(10,3,3,1), nrow=2,ncol=2)
colnames(tab) <- c("No_Therapy","Therapy")
row.names(tab) <- c("No_Prozac","Prozac")
tab[c("Prozac","No_Prozac"),c("Therapy","No_Therapy")]
#> Therapy No_Therapy
#> Prozac 1 3
#> No_Prozac 3 10