Dimethyl amine is Base. The basic character of it is due to the presence of lone pair of electron on nitrogen atom. The strength of amines is basically due to the presence of alkyl group attached to nitrogen atom. These alkyl groups donates electron to nitrogen atom hence increasing electron density on nitrogen and increasing its basic character.
When dimethylamine ( Kb = 5.9 × 10⁻⁴) is reacted with water it abstracts proton from water molecule convertion it into Hydroxide Ion (i.e ⁻OH). The reaction is as follow,
(CH₃)₂N + H₂O → (CH₃)₂N⁺H + ⁻OH
