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 det[[-a^(2),ab,acba,-b^(2),bcca,cb,-c^(2)]]=4a^(2)b^(2)c^(2)

Using properties of determinants, prove that |{:(0, ab^(2), ac^(2)),(a^(2)b, 0, bc^(2)),(a^(2)c, cb^(2), 0):}|=2a^(3)b^(3)c^(3)

Using properties of determinants,prove that: (a+b)^(2),ca,cbca,(c+b)^(2),abcb,ab,(c+a)^(2)]]=2abc(a+b+c)^(3)

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

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)

Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2