Examples:
$count = scalar(@matrix);
$count = @matrix;           # scalar() is optional since we're assigning to a scalar.
$count = $#matrix + 1;
$first_row = $matrix[0];    # this is a reference, rememeber..
@first_row = @$first_row;   # dereference it.
@first_row = @{$first_row}; # dereference it.
@first_row = @{$matrix[0]}; # dereference it.
$count_of_first_row = scalar(@first_row);     # scalar() is optional here.
$count_of_first_row = scalar(@{$matrix[0]});  # scalar() is optional here.
$first_field_of_second_row = $matrix[1][0];
$first_field_of_second_row = $matrix[1]->[0]; # this is what you are really doing.