Prove that: `|(a^2+1, ab, ac),(ab, b^2+1, bc),(ac, bc, c^2+1)|=1+a^2+b^2+c^2`

Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^2+ab, b^2, ac] , [ab, b^2+bc, c^2]| = 4a^2b^2c^2

What is |{:(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2)):}| equal to ?

Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=0

What is the value of |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))| ?

The determinant Delta =|(a^2(1+x),ab,ac),(ab,b^2(1+x),bc), (ac,bc,c^2(1+x))| is divisible by 1)1+x 2)(1+x)^2 3)x^2 4) x^2+1

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

The determinant Delta = |(a^(2) + x^(2),ab,ac),(ab,b^(2) + x^(2),bc),(ac,bc,c^(2) + x^(2))| is divisible