Prove that: `|[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2`

Prove that: |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=|[a^2+1,b^2,c^2],[a^2,b^2+1,c^2],[a^2,b^2,c^2+1]|=1+a^2+b^2+c^2

Using the properties of determinant, show that : |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]| = 1+a^2+b^2+c^2

Prove that: |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c^2

Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|= 2(a+b+c)^3

Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]| = |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

|[x^2+a^2,ab,ac] , [ab,x^2+b^2,bc] , [ac,bc,x^2+c^2]|=

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