Prove that `|[-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

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 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,ab,ac),(bc,-b^2,bc),(ca,cb,-c^2)|=4a^(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 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

Prove that: |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c^2