If `B ,C` are square matrices of order `n` and if `A=B+C` ,`BC=CB ,C^2=O ,` then without using mathematical induction, show that for any positive integer `p ,A^(p+1)=B^p[B+(p+1)C]` .

If B,C are square matrices of order n and if A=B+C,BC=CB,C^(2)=0 then which of the following is true for any positive integer N

If B,C are n rowed square matrices and if A=B+C,BC=CB,C^(2)=O, then show that for every n in N,A^(n+1)=B^(n)(B+(n+1)C)

Let B and C be two square matrices such that BC=CB and C^(2)=0 . If A=B+C then A^(3)-B^(3)-3B^(2)C is

Which of the following is/are true? If A is a square matrix such that A = A then (1 + A) - 7A=1 If A is a square matrix such that A = A then (1+4)° -7A=0 Let B and C be two square matrices such that BC = CB and C=0. If A = B+C then A - B -3B+C = 0 Let B and C be two square matrices such that BC = CB and C=0. If A = B+C then A+B -3B+C =0

If a^(2),b^(2),c^(2) are in A.P. ,then show that b+c,c+a,a+b are in H.P.

In A B C , P divides the side A B such that A P : P B=1:2 . Q is a point in A C such that P Q B C . Find the ratio of the areas of A P Q and trapezium B P Q C .

If a,b,c are first three terms of a G.P.If the harmonic mean of a and b is 20 and arithmetic mean of b&c is 5, then no term of this G.P.is square of an integer arithmetic mean of a,b,c is 5 c.b=+-6 d.common ratio of this G.P.is 2

If a,b,c are in H.P.show that (a-b)/(b-c)=(a)/(c)