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If A^(-1)=[(3,-1,1),(-15,6,-5),(5,-2, 2)...

If `A^(-1)=[(3,-1,1),(-15,6,-5),(5,-2, 2)]`and `B=[(1, 2,-2),(-1, 3, 0),( 0,-2, 1)]`, find `(A B)^(-1)`.

Text Solution

Verified by Experts

`|B|=1`
`adj B=[[3, 2, 6], [1, 1, 2], [2, 2, 5]]`
`B^(-1)=frac{adj B}{|B|}=[[3, 2, 6], [1, 1, 2], [2, 2, 5]]`
`(AB)^(-1)=B^(-1)A^(-1)`
`=[[3, 2, 6], [1, 1, 2], [2, 2, 5]] [[3, -1, 1], [-15, 6, -5], [5, -2, 2]]`
`=[[9, -3, 5], [-2, 1, 0], [1, 0, 2]]`
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