I have a dataset named DM with p1, p2, ...., p9 (9 columns, numerical values)
I would like to calculate to multify each pair of columns (p1p2, p1p3,...
p1p9, p2p3, p2p4.... p8p9) and assign them in p1p2, p1p3,... p1p9, p2p3,
p2p4.... p8p9

In SAS,

l=0;
p_int_sum=0;	
do i=1 to 8;
	do j=(i+1) to 9;
	l=l+1;
	p{i}p{j}=p{i}*p{j};
	end;
end;

I would like to know how to assign them in R 
I tried for function but failed.
for (i in 1:8) {
for (j in 2:9) {
DM$p[i]p[j] <- DM$p[i] * DM$p[j]

}}

Thank you so much for reading this!

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