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If A=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1...

If `A=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1)[[1//2,-1//2,1//2],[-4,3,b],[5//2,-3//2,1//2]]` then find `a` and `b`

A

1, 1

B

1, -1

C

1, 2

D

`-1, 1`

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`I=A A^(-1)=1/2 [(0,1,2),(1,2,3),(3,a,1)][(1,-1,1),(-8,6,2c),(5,-3,1)]`
`=[(1,0,c+1),(0,1,2(c+1)),(4(1-a),2(a-1),2+ac)]`
Comparing the elements of `A A^(-1)` with those of `I`, we have
`c+1=0` or `c=-1`
`a-1=0` or `a=1`
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