If `P={:[(2,-2,-4),(-1,3,4),(1,-2,-3)]:}` then show that, `p^(2)=p`.

If P=[{:(2,-2,-4),(-1,3,4),(1,-2,-3):}] , then P^(5) equals-

If P={:[(-1,3,5),(1,-3,-5),(-1,3,5)], show that, P^(2)=P hence find matrix Q such that 3P^(2)-2P+Q=I , where I is the unit matrix of order 3.

If p_(1),p_(2) be the lenghts of perpendiculars from origin on the tangent and the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) drawn at any point on it, show that, 4p_(1)^(2)+p_(2)^(2)=a^(2)

If p - frac(1)(p) = m then let's show that (p + frac(1)(p))^2 = m^2 + 4

Let p(x)=x^(2)-4x+3 . Find the value of p(0),p(1),p(2),p(3) and obtain zeroes of the polynomial p(x) .

If the coefficients of the pth , (p+1)and (p+2) terms in the expansions of (1+x)^(n) are in A.P , show that , n^(2)-n(4p+1)+4p^(2)-2=0

Using formula, let's solve each of the following problems- If m-frac(1)(m) = p - 2 , then lets show m^2 + frac(1)(m^2) = p^2 - 4p + 6

If p sin (alpha+ beta)= cos (alpha-beta) , then show that (1)/(1- p sin2 alpha)+(1)/(1-p sin 2 beta)=(2)/(1-p^(2)) .

If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

If P(A)=(2)/(3), P(B)=(1)/(2), P(A cap B)=(1)/(6) , then find the value of P(A cap B) and P(A cup B)