" 14."|[a^(2)+1,ab,ac],[ab,b^(2)+1,bc],[ca,cb,c^(2)+1]|

Using properties of determinants, prove the following: |[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2

Prove that |[-a^(2),ab,ac],[ba,-b^(2),bc],[ca,cb,-c^(2)]|=4a^(2)b^(2)c^(2)

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

By using properties of determinants , show that : {:[( a^(2) + 1, ab,ac),(ab,b^(2) + 1,bc),( ca, cb, 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 properties of determinant prove that |(a^(2)+1, ab, ac),(ab, b^(2)+1, bc),(ca, cb,c^(2)+1)|=(1+a^(2)+b^(2)+c^(2)) .

Prove that abs{:(a^(2) + 1, ab , ac),(ab, b^(2) + 1, bc),(ca, cb, c^(2) +1):}=1 + a^(2) + b^(2) +c^(2)

If D=|(a^(2)+1,ab,ac),(ba,b^(2)+1,bc),(ca,cb,c^(2)+1)| then D equal to

Using properties of determinants, prove that : |{:(a^(2)+1,ab,ac),(ba,b^(2)+1,bc),(ca,cb,c^(2)+1):}|=a^(2)+b^(2)+c^(2)+1