Question

$[b\times cc\times aa\times b]=$

• A. [a, b, c]
• B. 2 [a, b, c]
• C. $[a,b,c{]}^2$
• D. \N

Answer 1

The correct option is C $[a,b,c{]}^2$

$[a\times bb\times cc\times a]=(a\times b).(b\times c)\times (c\times a)$
$=(a\times b).\left\{\right[(b\times c).a]c-[(b\times c).c\left]a\right\}=(a\times b).\left\{\right[a.(b\times c)]c-[b,c,c\left]a\right\}=(a\times b).\left\{\right[a,b,c]c-0\}=[a,b,c]\left\{\right(a\times b).c\}=[a,b,c{]}^2$