Show without expanding at any stage that: ` [x,a,x+a],[y,b,y+b],[z,c,z+c]|=0 `

Show without expanding at any stage that: [x+y,y+z,z+x],[z,x,y],[1,1,1]|=0

Show without expanding at any stage that: [1,a,b+c],[1,b,c+a],[1,c,a+b]|=0

Show without expanding at any stage that: [0,a,-b],[-a,0,-c],[b,c,0]|=0

Show without expanding at any stage that: [1/a, a,bc],[1/b,b,ca],[1/c, c, ab]|=0

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

Show without expanding at any stage that: det [ [a,b,c],[a+2x,b+2y,c+2z],[x,y,z]] =0

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

Without expanding show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Without expanding , show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+a):}|=0

Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=0 .