Home
Class 12
MATHS
Let A=[[0, 1],[ 0, 0]]show that (a I+b ...

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`.

Text Solution

Verified by Experts

Given `A=[[1,0],[0,1]]`
To prove that `(a I+b A)^n=a^n I+n a^(n-1)b A`,
let n=1
`P(I):(aI+bA)=aI+ba^ 0 A=aI+bA`
The redult is true for n=1
let n=k
...
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If A=[0100], prove that (aI+bA)^(n)=a^(n)I+na^(n-1)bA where I is a unit matrix of order 2 and n is a positive integer.

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.

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

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.

Matrix A such that A^(2)=2A-I, where I is the identity matrix,the for n>=2.A^(n) is equal to 2^(n-1)A-(n-1)l b.2^(n-1)A-I c.nA-(n-1)l d.nA-I

If A be a real skew-symmetric matrix of order n such that A^(2)+I=0 , I being the identity matrix of the same order as that of A, then what is the order of A?