MCQ
If $a\,.\,b = a\,.\,c,\,\,a\, \times b = a \times c$ and $a \ne 0,$ then
- A$b = 0$
- B$b \ne c$
- ✓$b = c$
- DNone 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 $a \ne 0.$
(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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