The trace of a square matrix a is the sum of the diagonal entries in a and is denoted by tr a. it can be verified that tr(fg)equalstr(gf) for any two n times n matrices f and g. show that if a and b are similar, then tr upper a equals tr upper b.

Answer with Step-by-step explanation:

We are given that tr(FG)=tr(GF) for any two matrix of order

We have to show that if A and B are similar then

tr upper A=tr upper B

Trace of a square matrix A is the sum of diagonal entries in A and denoted by tr A

We are given that A and B are similar matrix  then there exist a inverse matrix P such that

Then

Let and F=AP

Then=A

GF=

We are given that tr(FG)=tr(GF)

Therefore, tr upper A=trB

Hence, proved

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step-by-step explanation: