Antima Jangid posted an Question
January 04, 2022 • 12:14 pm 30 points
  • IIT JAM
  • Mathematics (MA)

11. if p and are invertible matrices such that po=-qp, then we can conclude that (a) tr (p) =tr (q) =0 (b) tr(p)=tr(0)=1 (c)tr(p)=-tr(0) (d) tr(p)*tr(0)

11. If P and are invertible matrices such that PO=-QP, then we can conclude that (a) Tr (P) =Tr (Q) =0 (b) Tr(P)=Tr(0)=1 (c)Tr(P)=-Tr(0) (d) Tr(P)*Tr(0)

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  • Anonymous User best-answer

    Pre-multiply by P−1 to get Q=P−1(−Q)P which implies that matrices Q and −Q are similar, so tr(Q)=tr(−Q)⟹tr(Q)=0. Similarly you can get tr(P)=0 also

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