Let `A=[[0,2q,r] , [p,q,-r] , [p,-q,r]]` If `A A^T=I_3` then `|p|=`

Let A=|{:(,0,21,r),(,p,q,-r),(,p,-q,r):}|=A A^(T)=I_(3) then |p| is

Suppose p,q,r in R and and pqr = 2.5 . Let A = [(p,q,r),(r,p,q),(q,r,p)] If "AA"= I_(3) then maximum possible value of p^(3)+q^(3)+r^(3) is

[[ 0 , p-q , p-r ],[q-p , 0 , q-r],[ r-p , r-q , 0 ]] =

If A = |{:(p,q,r),(r,p,q),(q,r,p):}|and A A ^(T) = I "then" p^(3) + q^(3) + r^(3) =

|(0,p-q,p-r),(q-p,0,q-r),(r-p,r-q,0)|=

p,q,q,r Show that ,q,p,,q,r,r,p,r,q

If p,q,r are in H.P. and p,q,-2r are in G.P. ( p,q,r, gt0) then

Without expanding at any stage, prove that |(p+q, q+r, r+p),(q+r, r+p, p+q),(r+p, p+q, q+r)| = 2|(p,q,r),(q,r,p),(r,p,q)| .