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For the following pair of matrix veri...

For the following pair of matrix verify that `(A B)^(-1)=B^(-1)A^(-1)` . `A=[2 1 5 3]` and `B=[4 5 3 4]`

Text Solution

Verified by Experts

`|A|=1`
`A^(-1)=[[3, -1], [-5, 2]]`
`|B|=-1`
`B^(-1)=[[4, -5], [-3, 4]]`
`AB=[[11, 14], [29, 37]]`
`|AB|=1`
`(AB)^(-1)=[[37, -14], [-29, 11]]`
`B^(-1)A^(-1)=[[37, -14], [-29, 11]]`
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