`|[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

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]|

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]]

If A=[[a^2,ab,ac],[ab,b^2,bc],[ac,bc,c^2]] and a^2+b^2+c^2=1, then A^2

Show that | [a^2 +lambda, ab, ac], [ab, b^2+lambda, bc], [ac, bc, c^2+lamda]| is divisible by lambda^2 and find the other factor

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^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=lambda a^2b^2c^2 then find the value of lambda

The determinant Delta = |(a^(2) + x^(2),ab,ac),(ab,b^(2) + x^(2),bc),(ac,bc,c^(2) + x^(2))| is divisible

If a, b, c are real numbers, then find the intervals in which : f(x)=|(x+a^(2),ab,ac),(ab,x+b^(2),bc),(ac,bc,x+c^(2))| is strictly increasing or decreasing.