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

Using the property of determinants and without expanding,prove that: det[[x,a,x+ay,b,y+bz,c,z+c]]=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: |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: |[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: |[b+c, q+r, y+z],[ c+a, r+p, z+x],[ a+b, p+q, x+y]|=2|[a, p, x],[ b, q ,y],[ c, r, z]|

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-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: |[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 {:[( x,a,x+a),( y,b,y+b),(z,c,z+c)]:} =0