" 1."|[a-b,b-c,c-a],[x-y,y-z,z-x],[p-q,q-r,r-p]|" is equal to "

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

If |[p,q-y,r-z],[p-x,q,r-z],[p-x,q-y,r]|=0 find the value of p/x+q/y+r/z

If Delta_(1)=|[a,b, c],[x, y, z],[p,q ,r]|"and "Delta_(2) |[q,-b, y],[-p, a, -x],[r,-c ,z]| then without expanding Delta_(1) " and "Delta_(2), "prove that "Delta_(1) + Delta_(2) =0

If Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|, without expending or evaluating Delta_1 and Delta_2 , show that Delta_1+Delta_2=0

If A = [[a,b,c],[x,y,z],[p,q,r]], B= [[q , -b,y],[-p,a,-x],[r,-c,z]] and if A is invertible, then which of the following is not true?

If |[a, p, x],[ b, q, y], [c, r, z]|=16 , then the value of |[p+x, a+x, a+p], [q+y ,b+y, b+q],[ x+z, c+z, c+r]| is 4 (b) 8 (c) 16 (d) 32

If a=xy^(p-1),b=yz^(q-1),c=zx^(r-1) , then a^(q-r)b^(r-p)c^(p-q) is equal to