Prove the identities: `|[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]|` `=(a+b-c)(b+c-a)(c+a-b)`

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

Prove that: |(a,b-c,c-b),(a-c,b,c-a),(a-b,b-a,c)|=(a+b-c)(b+c-a)(c+a-b)

|[a-b, b-c, c-a], [b-c, c-a, a-b], [c-a, a-b, b-c]|=?

Prove that |[a+b+c, -c, -b],[-c, a+b+c, -a],[-b, -a, a+b+c]|=2(a+b)(b+c)(c+a)

Prove that |[a,b-c,c+b],[a+c,b,c-a],[a-b,a+b,c]|=(a+b+c)(a^2+b^2+c^2)

Evaluate the following: |[a-b, b-c, c-a],[b-c, c-a, a-b],[c-a, a-b, b-c]|

Prove the identities: |[a^2,a^2-(b-c)^2,b c], [b^2,b^2-(c-a)^2,c a],[ c^2,c^2-(a-b)^2,a b]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

Prove that det[[a-b,b-c,c-ab-c,c-a,a-bc-a,a-b,b-c]]=0

Evaluate abs([a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c])

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)