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Vijay posted an Question

May 02, 2021 • 20:20 pm

30 points

IIT JAM
Mathematics (MA)

Please send the solution to the problem given in the attachment.

2 Answer(s)

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A
Alka gupta

ans A,B,D...
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how do you know this?
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this is property of rank of a matrix if A is mxn order matrix then Rank(A) <= min { m,n}
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how, please show it
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4th equation
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is that also a property of rank of a matrix?
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if A and B are inverse of each other then rank will be same of both matrices
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>
Deepak singh 1 Best Answer

option a,b d are correct .
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I got it
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in this way
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why did you write this?
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no need of this ..
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can you please show that it is indeed true
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this is a result . Its general proof is long . You can find in any reference book.
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okay
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presumably my last doubt
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because rank A and Rank B is less than or equal to 5 and also we have to take minimum of A,B and that minimum is equal to 5 . Then its possible only when R(A)=R(B)=5 . let if any of R(A) and R(B) is less than 5 (I.e 4 say ) than minimum will be 4 and R(AB) is less than equal to 4 which is contradiction. So R(A)=R(B) =5
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