If you are always going to be accessing arbitrary rows and columns, not whole rows at once, you could consider using perl4's emulated multidimensional arrays (see $;), like so:

my %matrix;
$matrix{0,0} = 1;
$matrix{0,1} = 0;
$matrix{1,1} = 1;
$matrix{1,0} = 0;
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Then copying is just a matter of saying my %new_matrix = %$matrix_ref;