Home
Class 12
MATHS
Let P be an m xx m matrix such that P^2 ...

Let `P` be an `m xx m` matrix such that `P^2 = P`. Then `(1+P)^n` equals

A

`I +P`

B

`I + nP`

C

`I + 2^(n) P`

D

`I + (2^(n)-1)P`

Text Solution

Verified by Experts

The correct Answer is:
D
`P^(2)=P`
`P^(-1)P^(2)=P^(-1)P`
`P=I`
`(I+P)^(n)=(2P)^(n)=2^(n)P^(n)`
`=2^(n)P`
`=P+(2^(n)-1)P`
`=I+(2^(n)-1)P`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let P be a non - singular matrix such that I+P+P^(2)+…….P^(n)=O (where O denotes the null matrix), then P^(-1) is

If P = {2, 3}, then P xx P is equal to

Let omega be a complex cube root of unity with omega ne 0 and P=[p_(ij)] be an n x n matrix with p_(ij)=omega^(i+j) . Then p^2ne0 when n is equal to :

Let P be a matrix of order 3xx3 such that all the entries in P are from the set {-1,0,1} .Then,the maximum possible value of the determinant of P is

Let omega be a complex cube root of unity with omegane1 and P = [p_ij] be a n × n matrix with p_(ij) = omega^(i+j) . Then P^2ne0, , when n =

Let P be a non-zero polynomial such that P(1+x)=P(1-x) for all real x, and P(1)=0. Let m be the largest integer such that (x-1)^m divides P(x) for all such P(x). Then m equals

Let p be a non singular matrix,and I+P+p^(2)+...+p^(n)=0, then find p^(-1)