Let `A=[0 1 0 0]`show that `(a I+b A)^n=a^n I+n a^(n-1)b A`, where I is the identitymatrix of order 2 and `n in N`.

Let A=[[0, 1],[ 0, 0]] show that (a I+b A)^n=a^n I+n a^(n-1)b A , where I is the identity matrix of order 2 and n in N .

If A=[0 1 0 0] , prove that (a I+b A)^n=a^n\ I+n a^(n-1)\ b A where I is a unit matrix of order 2 and n is a positive integer.

Let A and B be matrices of order n. Prove that if (I - AB) is invertible, (I - BA) is also invertible and (I-BA)^(-1) = I + B (I- AB)^(-1)A, where I be the identity matrix of order n.

If A^(n) = 0 , then evaluate (i) I+A+A^(2)+A^(3)+…+A^(n-1) (ii) I-A + A^(2) - A^(3) +... + (-1) ^(n-1) for odd 'n' where I is the identity matrix having the same order of A.

Evaluate sum_(n=1)^(13)(i^n+i^(n+1)), where n in Ndot

Evaluate sum_(n=1)^(13)(i^n+i^(n+1)), where n in Ndot

If I_n is the identity matrix of order n then (I_n)^-1 (A) does not exist (B) =0 (C) =I_n (D) =nI_n

If (5 + 2 sqrt(6))^(n) = I + f , where I in N, n in N and 0 le f le 1, then I equals

If A=[(a, b),(0, 1)] , prove that A^n=[(a^n,b((a^n-1)/(a-1))),(0 ,1)] for every positive integer n .

If B_(0)=[(-4, -3, -3),(1,0,1),(4,4,3)], B_(n)=adj(B_(n-1), AA n in N and I is an identity matrix of order 3, then B_(1)+B_(3)+B_(5)+B_(7)+B_(9) is equal to