Using the property of determinants and without expanding, prove that:`|[a-b,b-c,c-a],[ b-c,c-a ,a-b ],[c-a ,a-b,b-c]|=0`

Using the property of determinants and without expanding,prove that: det[[a-b,b-c,c-ab-c,c-a,a-bc-a,a-b,b-c]]=0

Using the property of determinants and without expanding, prove that: |0a-b-a0-c b c0|=0

Using the property of determinants and without expanding, prove that: |[0,a,-b],[-a,0,-c],[ b, c,0]|=0

Using the property of determinants and without expanding , prove that: : |[0,a,-b],[-a,0,c],[b,c,0]| = 0

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

Using the property of determinants and without expanding,prove that: det[[0,a,-b-a,0,-cb,c,0]]=0

Using the property of determinants and without expanding {:[( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)]:} =0

Using the property of determinants and without expanding {:[( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)]:} =0

Using the property of determinants and without expanding {:|( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)|:} =0

Using the property of determinants and without expanding, prove that: |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b, c(a+b)]|=0