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

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)

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

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

Prove that |{:(p^(2)+1,pq,pr),(pq,q^(2)+1,qr),(pr,qr,r^(2)+1):}|=1+p^(2)+q^(2)+r^(2)

Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

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)

if bc+ qr= ca+rp = ab+ pq =-1 then prove that |{:(ap,,a,,p),(bq,,b,,q),(cr,,c,,r):}|=0

Show that : [[1+p,1,1],[1,1+q,1],[1,1,1+r]] = pqr (1+1/p+1/q+1/r)