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^(2) - A + I = 0 then A^(-1) is equal to

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=[(1,-3), (2,k)] and A^(2) - 4A + 10I = A , then k is equal to

If A^(2)-3A+2I=0 then

If A^(2)-3A+2I=0 , then A =

If a matrix A is such that 3A^(3)+2A^(2)+5A+I=0, then A^(-1) is equal to

If z=2+3i , then |z^2|^3 is equal to