3 deleted 1 character in body
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Jelly, 12 bytes

⁴Ḷ×þ`d⁴‘ịØhG

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How it works

⁴Ḷ×þ`d⁴‘ịØhG  Main link. No arguments.

⁴             Set the return value to 16.
 Ḷ            Unlength; yield [0, ..., 15].
  ×þ`         Build the multiplication table of [0, ..., 15] and itself.
     d⁴       Divmod 16; yield [p : 16, p % 16] for each product p.
       ‘      Increment quotients and remainders (1-based indexing).
        ịØh   Index into the lowercase hexadecimal alphabet.
           G  Grid; join columnsscolumns by spaces, rows by newlines.

Jelly, 12 bytes

⁴Ḷ×þ`d⁴‘ịØhG

Try it online!

How it works

⁴Ḷ×þ`d⁴‘ịØhG  Main link. No arguments.

⁴             Set the return value to 16.
 Ḷ            Unlength; yield [0, ..., 15].
  ×þ`         Build the multiplication table of [0, ..., 15] and itself.
     d⁴       Divmod 16; yield [p : 16, p % 16] for each product p.
       ‘      Increment quotients and remainders (1-based indexing).
        ịØh   Index into the lowercase hexadecimal alphabet.
           G  Grid; join columnss by spaces, rows by newlines.

Jelly, 12 bytes

⁴Ḷ×þ`d⁴‘ịØhG

Try it online!

How it works

⁴Ḷ×þ`d⁴‘ịØhG  Main link. No arguments.

⁴             Set the return value to 16.
 Ḷ            Unlength; yield [0, ..., 15].
  ×þ`         Build the multiplication table of [0, ..., 15] and itself.
     d⁴       Divmod 16; yield [p : 16, p % 16] for each product p.
       ‘      Increment quotients and remainders (1-based indexing).
        ịØh   Index into the lowercase hexadecimal alphabet.
           G  Grid; join columns by spaces, rows by newlines.
2 added 523 characters in body
source | link

Jelly, 12 bytes

⁴Ḷ×þ`d⁴‘ịØhG

Try it online!

How it works

⁴Ḷ×þ`d⁴‘ịØhG  Main link. No arguments.

⁴             Set the return value to 16.
 Ḷ            Unlength; yield [0, ..., 15].
  ×þ`         Build the multiplication table of [0, ..., 15] and itself.
     d⁴       Divmod 16; yield [p : 16, p % 16] for each product p.
       ‘      Increment quotients and remainders (1-based indexing).
        ịØh   Index into the lowercase hexadecimal alphabet.
           G  Grid; join columnss by spaces, rows by newlines.

Jelly, 12 bytes

⁴Ḷ×þ`d⁴‘ịØhG

Try it online!

Jelly, 12 bytes

⁴Ḷ×þ`d⁴‘ịØhG

Try it online!

How it works

⁴Ḷ×þ`d⁴‘ịØhG  Main link. No arguments.

⁴             Set the return value to 16.
 Ḷ            Unlength; yield [0, ..., 15].
  ×þ`         Build the multiplication table of [0, ..., 15] and itself.
     d⁴       Divmod 16; yield [p : 16, p % 16] for each product p.
       ‘      Increment quotients and remainders (1-based indexing).
        ịØh   Index into the lowercase hexadecimal alphabet.
           G  Grid; join columnss by spaces, rows by newlines.
1
source | link

Jelly, 12 bytes

⁴Ḷ×þ`d⁴‘ịØhG

Try it online!