Evaluate the following: ` |[0, ab^2, ac^2],[a^2b, 0, bc^2],[a^2c, cb^2, 0]| `

|{:(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2c,cb^2,0):}|=2a^3b^3c^3

Without expanding, prove the following |(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2b,b^2c,0)|=2a^3b^3c^3

|(0,ab^(2),ac^(2)),(a^(2)b,0,bc^(2)),(a^(2)c,b^(2)c,0)|=

Using properties of determinants, prove that |{:(0, ab^(2), ac^(2)),(a^(2)b, 0, bc^(2)),(a^(2)c, cb^(2), 0):}|=2a^(3)b^(3)c^(3)

Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,c-a,ab-a^2]]=0

Using properties of determinants, prove the following abs{:(a^2, bc, ac +c^2 ),(a^(2) + ab, b^(2),ac ),(ab, b^(2) + bc,c^(2) ):}=4a^(2) b^(2) c^(2) .

Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+b^2]]=4a^2b^2c^2

Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab, -ab]|=(ab+bc+ca)^2