If `A=[(3,-4),(1,-1)]` prove that `A^k=[(1+2k,-4k),(k,1-2k)]` where `k` is any positive integer.

If A=[[3,-41,-1]] prove that A^(k)=[[1+2k,-4kk,1-2k]] where k is any k integer.

If k is any positive integer, then (k^(2)+2k) is

Prove that sum_(k=1)^(n-1)(n-k)(cos(2k pi))/(n)=-(n)/(2) wheren >=3 is an integer

Prove that sum_(r=1)^(k)(-3)^(r-1)C(3n,2r-1)=0 where k=(3n)/(2) and n is an even positive integer.

Let A=[(2,0,7),(0,1,0),(1,-2,1)] and B=[(-k,14k,7k),(0,1,0),(k,-4k,-2k)] . If AB=I , where I is an identity matrix of order 3, then the sum of all elements of matrix B is equal to

If A = [{:(1,1),(1,1):}] and A ^(100) = 2k^(k) A, then the vlaue of k is

If (k-1),(2k+1),(6k+3) are in GP then k=?

If the middle term in the expreansion of (1+x)^(2n) is ([1.3.5….(2n-1)])/(n!) (k) , where n is a positive integer , then k is .