For what real number $b$, if any, will the equation $a-2b+ab=2$ be true for both $a=1$ and $a=-1$ ?

$-2$

$-1$

$1$

$2$

No such real number $b$ exists.

Approach

$$ a-2b+ab=2$$

$a=1$

$$ (1)-2b+(1)b=2$$ $$ 1-2b+b = 2 $$ $$ -b = 1 $$ $$ b= -1 $$

$a=-1$

$$ (-1)-2b+(-1)b=2$$ $$ -1-2b-b = 2 $$ $$ -3b=3 $$ $$ b= -1 $$