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

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

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

Without expanding the determinant, show that : (frac{1}{p}+frac{1}{q}+frac{1}{r}+1) is a factor of : |[[1+p,1,1],[1,1+q,1],[1,1,1+r]]

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

Show that the points : P (1, 2), Q (5, 4), R (3, 8) and S (-1, 6) are the angular points of a square PQRS.

For a matrix A=[[1,2r-1] , [0,1]] then prod_(r=1)^(60) [[1,2r-1] , [0,1]]=

Find r if : P(11,r) = P(12,r-1)

Show that the points :- P (3, 2), Q (0, - 1), R (- 3,- 2) and S (0, 1) are the vertices of parallelogram PQRS.