Hints:

1.) To prove this statement you must show:

a) If A is row equivalent to I2 then ad-bc is not equal to zero and
b) If ad-bc is not equal to zero then A is row equivalent to I2

This is the case for any 'if and only if' statement.

If I say 'p is true if and only if q is true', then I mean that:

If p is true then q is true and
If q is true then p is true

or:

p implies q and
q implies p

The 'if and only if' relationship is also called equivalence. Either both things are true or both things are false

2.) The notion ad-bc=0 is equivalent to the notion that the rows are multiples of each other. Watch:

  a  b    ac  bc    ac  bc
       ->        ->          since ad=bc
  c  d    ac  ad    ac  bc

3.) To prove

If A is row equivalent to I2 then ad-bc is not equal to zero

use the contrapostive. This means prove:

If ad-bd = 0 then A is not row equivalent to I2.

The contrapositive of the logical statement

'p implies q'

is the logical statement

'not q implies not p'.