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A and B are different matrices of order ...

A and B are different matrices of order n satisfying `A^(3)=B^(3)` and `A^(2)B=B^(2)A`. If det. `(A-B) ne 0`, then find the value of det. `(A^(2)+B^(2))`.

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`(A^(2)+B^(2))(A-B)=A^(3)-A^(2)B+B^(2)A-B^(3)=O`
`:.` det. `[(A^(2)+B^(2))(A-B)]=0`
`implies` det. `(A^(2)+B^(2))xx`det. `(A-B)=0`
`implies` det. `(A^(2)+B^(2))=0` (as det. `(A-B) ne0`)
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