" (i) "|[a^(2)+1,ab,ac],[ab,b^(2)+1,bc],[ac,bc,c^(2)+1]|=1+a^(2)+b^(2)+c^(2)

|(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-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) .

|(a^(2)+x,ab,ac),(ab,b^(2)+x,bc),(ac,bc,c^(2)+x)|

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+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

Show that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ca,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2)

Prove that |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))| = 4a^(2)b^(2)c^(2) .

Using the properties of determinant, 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 following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+a^2+b^2+c^2