If P={a,b} and Q={x,y,z}, show that `PxxQneQxxP.`

If P={:[(a,b),(c,d)]:}andQ={:[(w,x),(y,z)]:} , then show that (PQ)^(T)=Q^(T)P^(T) .

If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c-a).z(a-b)=1 .

If x^(1/a)=y^(1/b)=z^(1/c) where a,b,c are in A.P,,than show that x,y,z are in G.P.

If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.

If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.

If (y/z)^a.(z/x)^b.(x/y)^c=1 and a,b,c are in A.P ,show that x,y,z are in G.P.

If a,b,c,d are in A.P.and x,y,z are in G.P. then show that x^(b-c)*y^(c-a)*z^(a-b)=1

If p^(th) , q^(th) , r^(th) term of an A.P is x,y and z respectively. Show that x(q-r)+y(r-p)+z(p-q)=0

Let a(a != 0) is a fixed real number and (a-x)/(p x) = (a-y)/(qy) = (a-z)/(r z) . If p, q, r are in A.P., show that (1)/(x), (1)/(y), (1)/(z) are in A.P.

If the pth, qth and rt terms of an A.P. be x,y,z respectively show that: x(q-r)+y(r-p)+z(p-q)=0