If `A` is a nilpotent matrix of index 2, then for any positive integer `n ,A(I+A)^n` is equal to `A^(-1)` b. `A` c. `A^n` d. `I_n`

If A is a square matrix that |A|= 2, than for any positive integer n , |A^(n)|=

Derivative of f(x)=x^n is nx^(n-1) for any positive integer n.

If Aa n dB are square matrices of the same order and A is non-singular, then for a positive integer n ,(A^(-1)B A)^n is equal to A^(-n)B^n A^n b. A^n B^n A^(-n) c. A^(-1)B^n A^ d. n(A^(-1)B^A)^

Prove that n^(2)-n divisible by 2 for every positive integer n.

For any positive integer n, lim_(xtoa)(x^(n)-a^(n))/(x-a)=na^(n-1)

If a_(1), a_(2) …… a_(n) = n a_(n - 1) , for all positive integer n gt= 2 , then a_(5) is equal to

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to

Prove that (n !)^2 < n^n n! < (2n)! , for all positive integers n.

If k in R_ot h e ndet{a d j(k I_n)} is equal to K^(n-1) b. K^(n(n-1)) c. K^n d. k