The trace Tr( A) of a 3×3 matrix A=aij is defined by the relation Tr(A)=a11+a22+a33 (i.e., Tr(A) is sum of the main diagonal elements). Which of the following statements cannot hold '?

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Tr(kA)=kTr( A) (k is a scalar )

Tr(A+B)=Tr(A)+Tr(B)

TrI3=3

TrA2=Tr(A)2

answer is D.

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Detailed Solution

(a) Tr(kA)=ka11+a22+a33=kTr(A) (b) Tr(A+B)=a11+b11+a22+b22+a33+b33=TrA+TrBcTrI3=1+1+1=3dTrA2=Σa112+Σa122≠a11+a22+a332=TrA2

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