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 and hence show that its maximum value = 1

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

By using the properties of determinants,prove that |[a^2+1,ab ,ac],[ab,b^2+1,bc],[ca ,cb,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

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

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

|(a^(2)+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|= 1 + a^2 + b^2 + c^2 .