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Question

Let A =(p qrs] and B =(ab](00]. Such that AB = B and p+s = 2, then find the value of (ps-qr).

A
5
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B
1
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C
2
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D
3
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Solution

The correct option is B 1
Let A=(pqrs] and B=(ab]
Given AB = B. Thus,
(pqrs](ab]=(ab]or(pa+qbra+sb]=(ab]or pa+qb = a (1) ra+sb = b (2)Eliminating a,b from (1) and (2), we have(p1)a+qb = 0 ra+(s1)b = 0 or(p1qrs1](ab]=(00] (p1qrs1=0or( p1)(s1)qr=0or ps(p+s)+1qr=0or psqr=(p+s)1=21=1

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