my @mat1 = readmatrix ($first);
my ($r1, $c1) = ($rows, $cols);

...

sub readmatrix {
    my ($file) = @_;
    open(IN, "$file") || die "can't open file: $!\n";
    while (defined (my $line = <IN>)) {
        my @tmp = split(' ', $line);
        $cols = scalar @tmp;
        $rows++;
        push (@AoA, [@tmp]);
    }
    close IN;
}
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That would probably be better as:

my ( $r1, $c1, @mat1 ) = readmatrix( $first );

...

sub readmatrix {
    my ( $file ) = @_;
    open my $IN, '<', $file or die "can't open file: $!\n";
    my @AoA;
    while ( <$IN> ) {
        push @AoA, [ split ];
    }
    return $., scalar @{ $AoA[ -1 ] }, @AoA;
}
[download]