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If X = [{:(1,-2),(0,3):}], and I is a 2 ...

If `X = [{:(1,-2),(0,3):}]`, and `I` is a 2 `xx` 2 identity matrix, then `X^(2)-2X + 3I` equals to which one of the following ?

A

`-I`

B

`-2X`

C

`2X`

D

`4X`

Text Solution

Verified by Experts

The correct Answer is:
C
Given matrix is :
`X=[{:(1,-2),(0,3):}]`
`therefore X^(2)=[{:(1,-2),(0,3):}][{:(1,-2),(0,3):}]`
`=[{:(1,-2-6),(0," "9):}]=[{:(1,-8),(0,9):}]`
So, the given expression is :
`X^(2)-2X+3I=[{:(1,-8),(0,9):}]-2[{:(1,-2),(0,3):}]+3[{:(1,0),(0,1):}]`
`=[{:(1,-8),(0,9):}]+[{:(-2,+4),(0,-6):}]+[{:(3,0),(0,3):}]`
`=[{:(1-2+3,-8+4),(" "0,9-6+3):}]=[{:(2,-4),(0,6):}]=2[{:(1,-2),(0,3):}]`=2X`
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