Using properties of determinants, prove the following `|(a^2,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2`.

Using properties of determinants, prove the following |(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 determinants, prove that following: {:|(-a^2,ab,ac),(ba,-b^2,bc),(ac,bc,-c^2)|=4a^2b^2c^2

|(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 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

Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)|=4a^2 b^2 c^2

Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)|=4a^2 b^2 c^2

Using properties of determinants,prove the following: det[[a^(2),ab,acab,b^(2)+1,bcca,cb,c^(2)+1]]=1+a^(2)+b^(2)+c^(2)

Using properties of determinants,prove the following det[[a^(2),ab,acab,b^(2)+1,bcca,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)) .

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