Can a multiclass divine soul sorcerer / wizard add cleric spells to the spellbook?

I am in a campaign where I am a level 2 sorcerer and level 1 wizard and I have a paladin, a cleric, and a druid in my party. I was wondering if I am a divine sorcerer and have access to the cleric spell list, can the cleric or the paladin write cleric spells in my spellbook?
Or if I find or buy cleric spell scrolls can I add them to my spellbook?

Why? or Why not?