Using the properties of determinants show that : `|[[p^2, q^2, r^2],[qr,rp,pq],[p,q,r]]|=(p-q)(q-r)(r-p)(pq+qr+rp)`

Using the properties of determinant, show that : |[1,p+q,p^2+q^2],[1,q+r,q^2+r^2],[1,r+p,r^2+p^2]| = (p-q)(q-r)(r-p)

Show that: |[p-q-r,2p,2p],[2q,q-r-p,2q],[2r,2r,r-p-q]|=(p+q+r)^3

Prove that |[1,p,p^2-qr],[1,q,q^2-rp],[1,r,r^2-pq]|= 0

Using the property of determinants and without expanding , prove that: |[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]|

The value of |[[1,p,q+r],[1,q,r+p],[1,r,p+q]]| is

Using properties of determinants, prove that |b+c q+r y+z c+a r+p z+x c+b p+q x+y|=2\ |a p x b q y c r z|

Using the property of determinants and without expanding prove that : {:|(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y)|=2|(a,p,x),(b,q,x),(c,r,z)|

5pq(p^2 - q^2) -: 2p(p+q)

Show that Delta={:|(x,p,q),(p,x,q),(q,q,x)| = (x-p)(x^2+px-2q^2)