If a ,. ,b = a ,. ,c, , ,a , b = a c and a 0, then - Vidyadip

MCQ

If $a\,.\,b = a\,.\,c,\,\,a\, \times b = a \times c$ and $a \ne 0,$ then

A
$b = 0$
B
$b \ne c$
✓
$b = c$
D
None of these

✓

Answer

Correct option: C.

$b = c$

c
(c) $a\,.\,(b - c) = 0,$ $a \times (b - c) = 0 \Rightarrow b = c$ or $a = 0,$ but $a \ne 0.$

Hence $b - c = 0.$ i.e., $b = c$.

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