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# Is the product of A and B equal to 1? (1) A B A = A (2) B A

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Is the product of A and B equal to 1? (1) A B A = A (2) B A [#permalink]

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20 Nov 2007, 12:15
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Is the product of A and B equal to 1?

(1) A B A = A
(2) B A B = B
SVP
Joined: 01 May 2006
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20 Nov 2007, 12:28
(E) for me

A*B = 1 ?

Stat 1
A*B*A = A

We have 2 cases :
o If A =0 then 0*B*0 = 0 and A*B = 0*B = 0
o If A !=0 then A*B*A = A <=> A*B = 1

INSUFF.

Stat 2
B*A*B = B

We have 2 cases :
o If B =0 then 0*A*0 = 0 and A*B = A*0 = 0
o If A !=0 then B*A*B = B <=> A*B = 1

INSUFF.

Both 1 and 2
We still have 2 cases:
o If A = B = 0, then A*B*A = A = 0 and B*A*B = B = 0... as well as, A*B = 0
o If A = 1/B, then A*B*A = A and B*A*B = B... as well as, A*B = 1

INSUFF.
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