I'm not sure what you mean by "and everything else needs to be deleted". Does that means that rows with identical first column also have the exact same values for all the other columns, or that you want to somehow merge these identical rows into just one?
Assuming all duplicate rows are identical (but then why would you say unique values in one column?):
Assuming you want to just keep one arbitrary row out of the ones that have identical first column:
[~, rows] = unique(a(:, 1));
b = a(rows, :);
If you want to somehow merge the duplicate rows, it probably can be done but you need to give more details.