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

the determinant Delta=|[a^2+x, ab, ac] , [ab, b^2+x, bc] , [ac, bc, c^2+x]| is divisible by

The determinant "det(A)"= |[ a^(2) +x,ab,ac], [ab, b^(2) +x,bc,] [ac,bc, c^(2) +x]| is divisible by a. x b. x^2 c. x^3 d. none of these

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

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

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

Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

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

If A=[[0 ,c,-b],[-c, 0, a],[ b, -a, 0]] and B=[[a^2, ab, ac],[ ab, b^2 , bc],[ ac ,bc, c^2]] , show that A B=B A=O_3xx3 .

"If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," then prove that " f'(x)=3x^(2)+2x(a^(2)+b^(2)+c^(2)) .