[" 120MATHEMATICS "],[qquad |[0,a,-b],[-a,0,-c],[b,c,0]|=0]

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

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

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

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

Prove that : |{:(0,a-b,a-c),(b-a,0,b-c),(c-a,c-b,0):}|=0

Prove that : |{:(0,a-b,a-c),(b-a,0,b-c),(c-a,c-b,0):}|=0

Without expanding or evaluating show that |[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0

Evaluate |[0,c,b] , [c,0,a] , [b,a,0]| hence show that |[0,c,b] , [c,0,a] , [b,a,0]|^2= |[b^2+c^2,ab,ac] , [ab,c^2+a^2,bc] , [ca,bc,a^2+b^2]|=4a^2b^2c^2

If A=[(0,c,-b),(-c,0,a),(b,-a,0)] then A^(3)=