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: det[[0,a,-b-a,0,-cb,c,0]]=0

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: |[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: |[x, a ,x+a],[ y, b, y+b],[ z, c, z+c]|=0

Using the property of determinants and without expanding , prove that: |[2,7,65],[3,8,75],[5,9,86]| = 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^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: |[2, 7, 65],[ 3 ,8 ,75 ],[4, 9,86]|=0

Using the property of determinants and without expanding prove that abs([1,1,1],[a,b,c],[a^3,b^3,c^3])=(a-b)(b-c)(c-a)(a+b+c)