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Question

If a=b=c=1,a.b=b.c=c.a=12 then [a,b,c]=

A
1
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B
12
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C
12
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D
32
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Solution

The correct option is A 12
[a,b,c]2=⎢ ⎢ ⎢ ⎢a.aa.ba.cb.ab.bb.cc.ac.bc.c⎥ ⎥ ⎥ ⎥
=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢112121211212121⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
=1(114)12(1214)+12(1412)
=3412(14)+12(14)
=6118=48=12
[a,b,c]=12

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