× — Sign / Multiply

Function. Keys: Alt-m. Ranks: 0 monadic, 0 0 dyadic

×Y gives direction: zero, or Y÷|Y. The direction of a real number is an exact integer. Pervasive.

ׯ3 0 4           ⍝ [¯1 0 1]ₓ
×0j2              ⍝ 0j1

X×Y multiplies. Pervasive.

2ₓ×[1 2 3]ₓ       ⍝ [2 4 6]ₓ

Inverse

×⁻¹Y gives back Y when Y is a possible sign: ¯1, 0, 1 or a unit complex number. With either argument fixed, ×⁻¹ divides by the fixed argument, which must hold no zero.

×⁻¹¯1    ⍝ ¯1
4×⁻¹12   ⍝ 3