[" Prove the following "(17-32):],[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2|[a,b,c],[p,q,r],[x,y,z]|

Prove that the following. [[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2[[a,b,c],[p,q,r],[x,y,z]]

Prove that: |[b+c, c+a, a+b],[q+r, r+p, p+q],[y+z, z+x, x+y]|=2|[a,b,c],[p,q,r],[x,y,z]|

Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c],[p,q,r],[x,y,z]]

Without expanding, prove the following |(b+c,c+a,a+b),(q+r,r+p,p+q),(y+z,z+x,x+y)|=2|(a,b,c),(p,q,r),(x,y,z)|

Show that: |[b+c,c+a ,a+b],[ q+r, r+p, p+q],[ y+z ,z+x,x+y]|=2|[a, b, c],[ p, q, r],[ x, y, z]| .

Without expansion, prove the following: |(a+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)|

Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[z,c,r]]=[[x,y,z],[p,q,r],[a,b,c]]

Without expanding the determinant prove the following. |[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 Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,r+p,p+q),(y+z,z+x,x+y)|=2{:|(a,b,c),(p,q,r),(x,y,z)|