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=[[0,10,0]] show that (aI+bA)^(n)=a^(n)I+na^(n-1)bA where I is the identity matrix of order 2 and n in N

If I_(n) is the identity matrix of order n then (I_(n))^(-1)=

If A is idempotent matrix, then show that (A+I)^(n) = I+(2^(n)-1) A, AAn in N, where I is the identity matrix having the same order of A.

Let A and B be matrices of order n. Provce 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 dientity 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.

If A is a non zero square matrix of order n with det(I+A)!=0 and A^(3)=0, where I,O are unit and null matrices of order n xx n respectively then (I+A)^(-1)=

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

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

Show that (1-i)^(n)(1-(1)/(i))^(n)=2^(n) for all n in N