pairewise plots

Dear R users,

I have a data generated as the following,

dat <- data.frame(matrix(sample(24), nrow=4))
dimnames(dat) <-list(rownames=c('g1','g2','g3','g4'), colnames=c("A_CH1","A_CH2","B_CH1","B_CH2","C_CH3","C_CH3"))

? dat
  A_CH1 A_CH2 B_CH1 B_CH2 C_CH3 C_CH3
g1    16    24     7     9    14    20
g2     4    10    19    22     5    17
g3    11    18    21    12    13     1
g4     2     3    15     6    23     8

I am trying to plot them pairwise by column(might extend to more than 3 pairs) 
Instead manually plotting as below, could you please point me out with easier ways? 

par(mfrow=c(3,1))
plot(dat$A_CH1+dat$A_CH2, dat$A_CH1-dat$A_CH2)
plot(dat$B_CH1+dat$B_CH2, dat$B_CH1-dat$B_CH2)
plot(dat[,5]+dat[,6], dat[,5]-dat[,6])