|[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) .

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

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)=

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

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

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]|=|[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

Show that Delta=abs[[-a^2,ab,ac],[ba,-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 and hence show that its maximum value = 1