Prove the following theorems For any numbers a and b 2 a x b

Prove the following theorems. For any numbers a and b.

2. -a x -b = axb

Solution

1).

L.H.s = a/b

so 1/b can be written separately

= a. 1/b

L.H.S=R.H.S

2).

L.H.S= -ax-b

= -1xax-1xb

= -1x-1xaxb

= axb (since -1x-1 =1)

so L.H.S=R.H.S

3)

L.H.S= a/-b

= 1xa/-1xb

= -1xa/b

= -a/b

L.H.S=R,H,S