Home
Class 12
MATHS
Matrix A such that A^(2)=2A-I, where I i...

Matrix A such that `A^(2)=2A-I`, where I is the identity matrix, then for `n ge 2, A^(n)` is equal to

A

`n^(A)-n(n-1)`

B

nA-I

C

`2^(n-1)A-(n-1)I`

D

`2^(n-1)A-I`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise For Session 4|9 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise For Session 2|19 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

Write down the identity matrix of order 2.

If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisying the equation A A^(T)=9I , where I is 3xx3 identity matrix, then the ordered pair (a, b) is equal to

Let a be a 2xx2 matrix with non-zero entries and let A^(2)=I , where I is a 2xx2 identity matrix. Define Tr(A)= sum of diagonal elements of A and |A| = determinant of matrix A. Statement 1 : Tr (A) = 0 Statement 2 : |A|=1

Suppose A and B be two ono-singular matrices such that AB= BA^(m), B^(n) = I and A^(p) = I , where I is an identity matrix. If m = 2 and n = 5 then p equals to

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

Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[q_(ij)] is a matrix such that PQ=kI, where k in RR, k != 0 and I is the identity matrix of order 3. If q_23=-k/8 and det(Q)=k^2/2, then

Suppose A and B be two ono-singular matrices such that AB= BA^(m), B^(n) = I and A^(p) = I , where I is an identity matrix. Which of the following orderd triplet (m, n, p) is false?

If A is any of square matrix of order n, then A (adj A) is equal to

If a square matrix A is involutory, then A^(2n+1) is equal to: