Using properties of determinants , prove that,  `|{:(a,b,c),(b,c,a),(c,a,b):}|=-(a^3+b^3+c^3-3abc)`
Channel: Doubtnut
Date: 2020-05-09

Using properties of determinants , prove that,  `|{:(a,b,c),(b,c,a),(c,a,b):}|=-(a^3+b^3+c^3-3abc)`  and hence show that, `|{:(2bc-a^2,"    "c^2,"    "b^2),("  "c^2,2ca-b^2,"    "a^2),("  "b^2,"   "a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2`