Home
Class 12
MATHS
If A^(2) - 3 A + 2I = 0, then A is equal...

If `A^(2) - 3 A + 2I = 0,` then A is equal to

A

`I`

B

`2I`

C

`[[3,-2],[1,0]]`

D

`[[3,1],[-2,0]]`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`because A^(2) - 3 A + 2I = 0` …(i)
`rArr A^(2) - 2 AI + 2I^(2) = 0 `
`rArr (A-I) (A -2I) = 0`
`therefore A = I or A = 2I`
Characteristic Eq. (i) is
`lambda^(2) - 3lambda + 2 = 0 rArr lambda = 1,2`
It is clear that alternate (c) and (d) have the characteristic
equation `lambda^(2) - 3lambda + 2 = 0 `.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • MATRICES

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

If A is a square matrix of order 3 and I is an ldentity matrix of order 3 such that A^(3) - 2A^(2) - A + 2l =0, then A is equal to

If A^(2)-A+I=O , then A^(-1) is equal to

Let A be a square matrix of order 3 xx 3 , then I 2A I is equal to :

Fill in the blank: Let * be a binary operation defined on Z as a * b = a^2 - b^2 , then (-2)*(3*0) is equal to _______

If A is non-singular and (A-2I)(A-4I)=0 , then ,1/6A+4/3A^(-1) is equal to a. 0I b. 2I c. 6I d. I

If A is square matrix such that A^2 = A ,then (I+A)^3-7A is equal to:

If A=[[(-1+isqrt(3))/(2i),(-1-isqrt(3))/(2i)],[(1+isqrt(3))/(2i),(1-isqrt(3))/(2i)]] , i = sqrt(-1) and f (x) = x^(2) + 2, then f(A) equals to

If a + 2b + 3c= 0 , then axxb + bxxc+c xxa is equal to