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|(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-...

`|(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c)|=`

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|(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=

|(a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)|=

|(a+b,c,c),(b,a+c,b),(a,a,b+c)|=

|(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b)|=

|(a,b,c),(b,c,a),(c,a,b)|=

|(b+c,a+b,a),(c+a,b+c,b),(a+b,c+a,c)|=

Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c)(c+a)

|(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=

Without expanding the determinant show that |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2|(a,b,c),(b,c,a),(c,a,b)|