|[-2a,a+b,a+c],[b+a,-2b,b+c],[c+a,c+b,-2c]|

Using the property of determinants and without expanding, prove that: |[-a^2,a b, a c],[ b a, -b^2,b c],[c a, c b,-c^2]|=4a^2b^2c^2

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c)(c+a)

Prove that abs((-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c))=4(b+c)(c+a)(a+b)

Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]| = (a+b+c)(a^2+b^2+c^2)dot

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|

Find the value of the determinant |{:(a^2,a b, a c),( a b,b^2,b c), (a c, b c,c^2):}|

Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a b-c^2b c-a^2c a-b^2]|=|[a, b, c],[ b ,c ,a],[ c, a ,b]|^2 .

Show that |[a, b-c, c+b] , [a+c, b, c-a] , [a-b, b+a, c]|=(a+b+c)(a^2+b^2+c^2)