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Question

Let A+2B=120633531 and 2AB=215216012, then find tr(A) - tr(B).

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Solution

Given A+2B=120633531
tr(A+2B)=1
or tr(A)+2tr(B)=1 .............. (1)
Also given 2AB=215216012
tr(2AB)=3
or 2tr(A)tr(B)=3 ............ (2)
Solving (1) and (2), we get
tr(A)=1 and tr(B)=1
tr(A)tr(B)=2

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