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If A=[(2,3),(1,-2)] and A^(-1)=alphaA, t...

If `A=[(2,3),(1,-2)]` and `A^(-1)=alphaA,` then `alpha` is equal to

A

7

B

`-7`

C

`1/7`

D

`-1/7`

Text Solution

Verified by Experts

The correct Answer is:
C
Now `|A|=4-3=-7`
Now `A^(-1)=1/(|A|)adj A=1/(-7)[(-2,-3),(-1,2)]`
`=1/7[(2,3),(1,-2)]=1/7A`
`:'A^(-1)=alphaA`
`:.1/7A=alphaAimpliesalpha=1/7`
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