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`

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

Prove that [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] = 1+a^2+b^2+c^2 and hence show that its maximum value = 1

Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,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

Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

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

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