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Let A+2B=[(1,2,0),(6,-1,3),(-5,3,1)] and...

Let `A+2B=[(1,2,0),(6,-1,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,2)],` then find `tr(A)-tr(B).`

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Here to find the value of tr (A) - tr(B), we need not to find the matrices A and B.
We can find tr(A)-tr (B) using the properties of trace of matrix, i.e.,
`A+2B=[(1,2,0),(6,-3,3),(-5,3,1)]`
`implies tr (A+2B)=-1`
or `tr (A)+2tr (B)=-1` (1)
`2A-B=[(2,-1,5),(2,-1,6),(0,1,2)]`
`implies tr (2A-B)=3`
or `2tr (A)-tr (B) =3` (2)
Solving (1) and (2), we get tr(A)=1 and tr (B)=-1
`implies` tr(A)- tr (B)=2
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