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|{:(a-b,b-c,c-a),(x-y,y-z,z-x),(p-q,q-r,...

`|{:(a-b,b-c,c-a),(x-y,y-z,z-x),(p-q,q-r,r-p):}|=`

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Evaluate the following determinants: [[a-b,b-c,c-a],[x-y,y-z,z-x],[p-q,q-r,r-p]]

Prove that the value of each the following a=bquad b-cquad c-ax-y,y-z,z-xp-q,q-r,r-p]|

Prove that the value of determinants is zero: |a-b b-c c-a x-y y-z z-x p-q q-r r-p|

|{:(a,b,c),(x,y,z),(p,q,r):}|=|{:(x,y,z),(p,q,r),(a,b,c):}|=|{:(y,b,q),(x,a,p),(z,c,r):}|

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

|(a-b,p-q,x-y),(b-c,q-r,y-z),(c-a,r-p,z-x)|=

Without, prove that : |{:(1+b,b+c,c+a),(p+q,q+r,r+p),(x+y,y+z,z+x),:}|=2|{:(a,b,c),(p,q,r),(x,y,z):}|

If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)| , then