If `A={:((-2,-1),(-5,-3)):}B={:((-3,1),(5,-2)):}and(AB)^(n)=I` then n is (a/an)

If A = [(3,1),(5,2)] , and AB = BA = I, then find the matrix B.

(i) if A=[{:(1,-4),(3,1):}]and b=[{:(1,0,5),(-2,4,3):}], then show that : (AB)'=B'A' (ii) if A=[{:(2,3),(0,1):}]and B=[{:(3,4),(2,1):}], then prove that : (AB)'=B'A'

Let A = ((1,1,3),(5,2,6),(-2,-1,-3)) and let n be the smallest value of n in N such that A^(n) = O_(3) then det (I_(3)+A+A^(2)+ cdots+ A^(n-1)) is equal to _____ .

2n(AB)=n(BA) and 5(A nn B)=n(A)+3n(B)

If A&B are square matrices such that A+B=1,AB=1, and A^(6)-3A^(5)+3A^(4)-A^(3)+A^(2)-A= nI , then n^(2) is equal to

If A&B are square matrices such that A+B=I , AB=1 , and A^(6)-3A^(5)+3A^(4)-A^(3)+A^(2)-A = nl ,then n^(2) is equal to

If n>3 and a,b in R ,then the value of ab-n(a-1)(b-1)+(n(n-1))/(1.2)(a-2)(b-2)-.....+(-1)^(n)(a-n)(b-n) is equal to

Find the sum (i) 1+(-2)+(-5)+(-8)+ … +(-236) (ii) (4-(1)/(n))+(4-(2)/(n))+(4-(3)/(n))+ … upto n terms. (iii) (a-b)/(a+b)+(3a-2b)/(a+b)+(5a-3b)/(a+b)+ … to 11 terms.

Find the sum (i) 1+(-2)+(-5)+(-8)+ … +(-236) (ii) (4-(1)/(n))+(4-(2)/(n))+(4-(3)/(n))+ … upto n terms. (iii) (a-b)/(a+b)+(3a-2b)/(a+b)+(5a-3b)/(a+b)+ … to 11 terms.