The total number of matrices The total number of matrices A= 0       2y        12x      y     −12x    −y       1 (x,y∈R,x≠y) for which ATA=3I3 is 

The total number of matrices The total number of matrices A= 0      2y        12x     y    12x    y       1 (x,yR,xy) for which ATA=3I3 is

 

  1. A

    4

  2. B

    3

  3. C

    2

  4. D

    6

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    Solution:

    Given, ATA=3I3

    02x2x2yyy11102y12xy12xy1=31000100018x20006y20003=3000300038x2=3,6y2=3x2=38,y2=12x=±38,y=±12

     Required number of matrices is 4.

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