Without expanding the determinant prove that: `|0b-c-b0a c-a0|=0`

Without expanding the determinant prove that: {:|(0,a,-b),(-a,0,-c),(b,c,0)|:}=0

Without expanding the determinant , prove that |(s,a^(2),b^(2)+c^(2)),(s,b^(2),c^(2)+a^(2)),(s,c^(2),a^(2)+b^(2))|=0

Without expanding the determinant prove that |[s,a^(2),b^(2)+c^(2)],[s,b^(2),c^(2)+a^(2)],[s,c^(2),a^(2)+b^(2)]|=0

Without expanding the determinant prove the following. |[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|=0

Prove that: |0a-b-a0-cbc0|=0

Without expanding the determinant prove the following. |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

Without expanding the determinant prove the following. |[x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

Without expanding the determinant, show that (a+b+c) is a factor of the determinant |[a, b, c], [b, c, a], [c, a, b]|

Without expanding the determinant, show that (a+b+c) is a factor of the determinant |a b c b c a c a b| .

Without expanding determinant show that |(0,a,b),(-a,0,c),(-b,-c,0)|=0