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Symmetric Matrix Class 12th

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
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Payal Gupta

Contributor-Level 10

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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