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Grade 12th passEngineering Entrance Exams

Let Q and R be two matrices oforder 3 x 3 such that Qis not equal to R.if P is a matrix of order 3 X3 such that PQ = PR then (A) detQ=detR (B) detP=1. (C) det P = 0 (D) P is a zero matrix

Profile image of Anand Oganiya
9 Years agoGrade 12th pass
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2 Answers

Profile image of Saurabh Koranglekar
7 Years ago
Dear student

Ans is det p

By performing deterinant rows and coloumns operation we can obtain the result, kindly revert if problem persists

Regards
Profile image of Aditya Gupta
7 Years ago
We need to remember an important formula:
det(AB)= det(A)*det(B).
We are given that PQ=PR
Taking determinant both sides and rearranging we have
detP*(detQ-detR)=0
And hence detP=0
Note that detP definitely has to be zero but detQ-detR need not always be zero. Lets assume detP is not zero. That means it's inverse exists.
So P-1(PQ)= P-1(PR)
Q=R which is prohibited in the question.
Hence correct option is only C

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