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Find the matrix X satisfying the equat...

Find the matrix `X` satisfying the equation: `[[2 ,1], [5 ,3]]X[[5, 3] ,[3, 2]]=[[1, 0], [0 ,1]]` .

Text Solution

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`A=[[2, 1], [5, 3]]`, `B=[[5, 3], [3, 2]]` and `C=[[1, 0], [0, 1]]`
`AXB=I`
`X=A^(-1)B^(-1)`
`|A|=1` and `|B|=1`
`A^(-1)=[[3, -5].[-5, 2]]`
`B^(-1)=[[2, -3], [-3, 5]]`
`X=A^(-1)B^(-1)=[[9, -14], [-16, 25]]`
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