Chapter 1 pre-cal proofs help?

Question

i need help proving the 3 following proofs:

(-ab)= (-a)b = (-b)a

and

-(a+b)= -a + (-b)

and

if a =/= 0, 1/(-a) = (-1)/a = - 1/a

thank you!

Answer 1

(-ab)= (-a)b = (-b)a

(-ab)/b= (-a)b/b = (-b)a/b

-a = -a = -a

-a/a = -a/a = -a/a

-1 = -1 = -1

Q.E.D.

-(a+b) = -a + (-b)

-1(a+b) = -a + (-b)

-1(a) + (-1)b = -a + (-b)

-a + (-b) = -a + (-b)

Q.E.D.

if a ≠ 0, 1/(-a) = (-1)/a = - 1/a

[1/(-a)](a) = [(-1)/a]a = -(1/a)(a)

a/(-a) = (-1)a/a = -(a/a)

a/(-a) = (-1)a/a = -1(a/a)

a/-a = (-1)a/a = -1(a/a)

a/-1(a) = (-1)(1) = -1(1)

1/-1 = -1 = -1

-1 = -1 = -1

Quote Era Demonstratum

I suspect you can also prove these by inducton; but I don't know if you've studied that yet.