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

Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

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)

Using properties of determinants, 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 |[-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

Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]|=(a b+b c+a c)^3

Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2]|=4a^2b^2c^2

Show that |[0,c,b] , [c,0,a] , [b,a,0]|^2=|[b^2+c^2, ab, ac] , [ab, c^2+a^2, bc] , [ac, bc, a^2+b^2]|

If a, b and c are distinct positive real numbers such that Delta_(1) = |(a,b,c),(b,c,a),(c,a,b)| and Delta_(2) = |(bc - a^2, ac -b^2, ab - c^2),(ac - b^2, ab - c^2, bc -a^2),(ab -c^2, bc - a^2, ac - b^2)| , then

Find the product of the following two matrices [(0,c,-b),(c,0,a),(b,-a,0)] and [(a^2,ab,ac),(ab,b^2,bc),(ac,bc,c^2)] .

Find the product of the followng two matrices: [[0,c,-b],[-c,0,a],[b,-a,0]] and [[ a^2,ab,ac],[ab,b^2,bc],[ac,bc,c^2]]