Formal Proof Question

Q$7.$ The zero vector plays a very important role within linear alge$-$ bra. In this question you are going to prove two very important properties of the zero vector.

$($a$)$ The zero vector is unique. $($b$)$Foranyvector$$v in V andc in F$,$

$0=$ c $0=0$v $.$

$($Note: Most of the question has been proven informally in lec$-$ ture.$)$