Prove The Multiplicative Property of the Scalar Zero: 0 O V = (y. Hint: use the fact that 0 + 0) = 0.

Answer and Step-by-step explanation:

Proof: multiplicative property of scalar zero states that the product of any number and zero is zero.

So, 0 v= 0,

Let y be a field. We will denote one by an identity element and (-v) as an additive inverse of v.

0v = 0v + 0

=0v + (v + (-v)) by inverse element

= (0v + v) + (-v) by associative property of vector addition

= (0v + 1v) + (-v) by identity element of scalar multiplication

= (0 + 1) v + (-v) by distributive property of scalar multiplication

= (1v) + (-v) by identity element of scalar multiplication

= v + (-v) by inverse element of vector addition

=0

Hence proved.