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By using properties of determinants. Show that:`|1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^2)^3`

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`|{:(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),2ab,-2b),(2ab,1+a^(2)+b^(2),2ab),(b(1+a^(2)+b^(2)),-a(1+a^(2)+b^(2)),1+a^(2)+b^(2)):}|`
`(C_(1)toC_(1)-bC_(3),C_(2)toC_(2)+aC_(3))`
`=(1+a^(2)+b^(2))^(2)|{:(1,0,-2b),(0,1,2a),(b-a,1-a^(2),-b^(2)):}|`
`(C_(3)toC_(3)+2b.C_(1))`
`=(1+a^(2)+b^(2))^(2).1|{:(1,,2a),(-a,1-a^(2),+b^(2)):}|`
(Expanding along `R_(1)`)
`=(1+a^(2)+b^(2)+2a^(2))`
`=(1+a^(2)+b^(2))^(3)=R.H.S.`
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