|[0,a-b,a-c],[b-a,0,b-c],[c-a,c-b,0]|=0

Write the value of the determinant |(0,a-b,a-c), (b-a, 0, b-c),(c-a, c-b, 0)|

Prove that: |[0,a,-b],[-a,0,-c],[ b, c,0]|=0 .

If Delta= |[0,b-a,c-a],[a-b,0,c-b],[a-c,b-c,0]| then Delta=

If a+b+c=0, solve the equation: |[a-x, c, b],[c,b-x, a],[b, a, c-x]|=0

If |(a,-b,a-b-c),(-a,b,-a+b-c),(-a,-b,-a-b+c)| - kabc = 0 (a != 0, b != 0, c != 0) then what is the value of k ?

|(0,a,-b),(-a,0,-c),(b,c,0)| = 0

If a+b+c=0 and |[a-x,c,b],[c,b-x,a],[b,a,c-x]|=0 then x=

if abc!=0 and if |[a,b,c],[b,c,a],[c,a,b]|=0 then (a^3+b^3+c^3)/(abc)=

Show that det[[0,b-a,c-aa-b,0,c-ba-c,b-c,0]]=0

If a, b and c are real numbers, and triangle = |[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]| = 0 Show that either a+b+c = 0 or a=b=c