You didn't say which language you are using. I guess since you tagged it with awk and perl, that's what you want?

Anyway, if you were using R, you could do it with a call to table:

## Maybe you have this in a tab delimited file already
> dat <- read.table('/path/to/2-column-file.txt')
## but I'll generate a random table that looks close-enough to your data:
> set.seed(1)
> dat <- data.frame(x1=rep(c('m01', 'm02', 'm03'), each=10),
                    x2=sample(c('m01', 'm02', 'm03'), 30, replace=TRUE))
> head(dat)
    x1  x2
1| m01 m01
2| m01 m02
3| m01 m02
4| m01 m03
5| m01 m01
6| m01 m03

> table(dat$x1, dat$x2)
      m01 m02 m03
  m01   3   4   3
  m02   2   3   5
  m03   4   4   2

You won't get a matrix, but the answer would be the same.

sort 2-col.txt | uniq -c

Or with awk.

awk -v OFS="\t" '{cnt[$0]+=1} END{for (key in cnt) {print key,cnt[key]} }' 2-col.txt

Or with perl.

perl -lane '$cnt{$_}++; END { foreach $key (keys %cnt) {print "$key\t$cnt{$key}"} }' 2-col.txt