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If A=[(2,-1),(-1,2)] and l is the unit m...

If `A=[(2,-1),(-1,2)]` and `l` is the unit matrix of order 2, then `A^(2)` equals to

A

`4A-3l`

B

`3A-4l`

C

`A-l`

D

`A+l`

Text Solution

Verified by Experts

The correct Answer is:
A
If `A=[(2,-1),(-1,2)]`
`A^(2)=[(2,-1),(-1,2)][(2,-1),(-1,2)]`
`=[(4+1,-2-2),(-2-2,1+4)]=[(5,-4),(-4,5)]`
`:.4A-3l=4[(2,-1),(-1,2)]-3[(1,0),(0,1)]`
`=[(8,-4),(-4,8)]-[(3,0),(0,3)]=[(5,-4),(-4,5)]`
`:.A^(2)=4A-3l`
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