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Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A2 is 1, then the possible number of such matrices is

Option 1 -

1

Option 2 -

6

Option 3 -

4

Option 4 -

12

0 3 Views | Posted a month ago
Asked by Shiksha User

  • 1 Answer

  • P

    Answered by

    Payal Gupta | Contributor-Level 10

    a month ago
    Correct Option - 3


    Detailed Solution:

    A= [pqrs] is symmetric. So, q = r.

    AA=A2= [pqrs] [pqrs]= [p2+qrpq+qsrp+rsrq+s2]

    Sum of diagonal elements =

    p2+qr+rq+s2=1⇒p2+2r2+s2=1, (as  q=r), p=0, r=0  and  s=±1  or  r=0, s=0  and  p=±1

    Total number of matrices = 4.

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