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Shivam Kumar posted an Question
January 03, 2020 • 06:14 am 15 points
  • IIT JAM
  • Mathematics (MA)

SECTION-(C) NUMERICAL ANSWER TYPE QUESTIONs (NA) Mathematics (USP-12) (a b C dnere (ab - bc) # 0 and a, b, C, d are integers modulo If G is a group of all 2 x 2

SECTION-(C) NUMERICAL ANSWER TYPE QUESTIONs (NA) Mathematics (USP-12) (a b C dnere (ab - bc) # 0 and a, b, C, d are integers modulo If G is a group of all 2 x 2 matrices b 3, relative to matrix multiplication, then what is the number of element

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  • David best-answer

    Since the elements are from Z3.. The elements are 0,1,2 . since ad - bc is not equal to zero, the matrices are Non singular.... Therefore the rows of the matrix has to be linearly independent. The first row has 3^2 - 1 choices. That is 8 ways. That is each position has three choices. Therefore 3^2 choices minus the entry 0,0 since it linearly dependent. The second row should not be the multiple of first row.....if V is first row vector... Then the multiples are 0V,1V,2V.....therefore seconds row has 3^2-3 choices. That is 6 Ways. Therefore total 8×6=48 matrices

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