In your code, $a and $b are elements of @unsorted_array which are arrayrefs. You need to dereference them to get the actual element you want to sort on.

@unsorted_array = ([f, g, h, i, j], 
                   [a, b, c, d, e], 
                   [k, l, o, n, r], 
                   [j, a, o, n, e], 
                   [f, p, r, t, u]);

@big_table_array = sort {uc($a->[0]) cmp uc($b->[0])} @unsorted_array;
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