If `X=[[0, 1], [0, 0]]` , then prove that `(p I+q X)^m=p^m I+m p^(m-1)q X ,AAp ,q in R` ,where I is a two rowed unit matrix and `m in N.`

If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

Prove that p x^(q-r)+q x^(r-p)+r x^(p-q)> p+q+r ,where p, q, r are distinct and x!=1.

If p+r=mq and (1)/(q)+(1)/(s)=(m)/(r ), then prove that : p:q=r:s .

If A xxB = {(p , q), (p , r), (m , q), (m , r)} , find A and B.

If the points (p ,\ q),\ (m ,\ n) and (p-m ,\ q-n) are collinear, show that p n=q m .

If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, then prove that p+q+r=0 (where p ,q ,r are distinct ) .

If A xx B = {(p, q), (p, r), (m, q), (m, r)} , Find A and B

If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, then prove that p+q+r=0(where, p ,q ,r are distinct )dot

Given that q^2-p r ,0,\ p >0, then the value of |p q p x+q y q r q x+r y p x+q y q x+r y0| is- a. zero b. positive c. negative \ d. q^2+p r