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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 `.
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