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Using properties of determinants prove t...

Using properties of determinants prove that
`|{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}|=(a-1)^3`

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Answer any three questions Using properties of determinants, prove the following abs{:(1+a^2 - b^2,2ab,-2b),(2ab,1-a^(2) +b^(2) ,2a),(2b,-2a,1-a^2 -b^2):}=(1+a^2 +b^2)^3.

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Using the properties of determinants, show that abs[[1+a^2-b^2,2ab,-2b],[2ab,1-a^2+b^2,2a],[2b,-2a,1-a^2-b^2]]=(1+a^2+b^2)^3

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Evaluate the following determinants |{:(1,1,1),(2,2,2),(3,3,3):}|