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

Using the property of determinants and without expanding,prove that: det[[1,bc,a(b+c)1,ca,b(c+a)1,ab,x(a+b)]]=0

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

Using the property of determinants and without expanding prove that {:|( 1,bc,a(a+c) ),(1,ca,b( c+a)) ,( 1,ab,c(a+b) )|:}=0

Using the property of determinants and without expanding, prove that: |-a^2a b a c b a b^2b cc 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, 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 {:|( 0,a,-b),(-a,0,-c),( b,c,0) |:}=0