Let `A=[(0,1),(0,0)]`, 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`.

A square matrix P satisfies P^(2)=I-P , where I is identity matrix. If P^(n)=5I-8P , then n is :

A square matrix M of order 3 satisfies M^(2)=I-M , where I is an identity matrix of order 3. If M^(n)=5I-8M , then n is equal to _______.

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

Let n ge 2 be an integer, A=({:(cos((2pi)/(n)),sin((2pi)/(n)),0),(sin((2pi)/(n)),cos((2pi)/(n)),0),(0,0,1):}) and I is the idnetity matrix of order 3. Then

Value of i^n+i^(n+1)+i^(n+2)+i^(n+3) (where i=sqrt-1 )

Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4) , where n is a positive integer.

If A={:[(1,2),(0,1)]:} show, by mathematical induction, that A^(n)={:[(1,2n),(0,1)]:} for all n in N.

If A=[[-1, 1],[ 0,-2]] , then prove that A^2+3A+2I=Odot Hence, find Ba n dC matrices of order 2 with integer elements, if A=B^3+C^3dot

If A=[(a,b),(0,a)] is nth root of I_(2) , then choose the correct statements : (i) if n is odd, a=1, b=0 (ii) if n is odd, a=-1, b=0 (iii) if n is even, a=1, b=0 (iv) if n is even, a=-1, b=0

Let a_(0)=0 and a_(n)=3a_(n-1)+1 for n ge 1 . Then the remainder obtained dividing a_(2010) by 11 is