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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=[(3, 2),( 7 ,5)]` and `B=[(4, 6),( 3, 2)]`

Text Solution

Verified by Experts

`A=[[3, 2], [7, 5]]`
`B=[[2, -6], [-3, 4]]`
`adj A=[[5, -2][-7, 3]]`
`A^(-1)=[[5, -2][-7, 3]]`
`adj B=[[2, -6], [-3, 4]]`
`B^(-1)=-1/10 [[2, -6], [-3, 4]]`
`AB=[[18, 22], [43, 52]]`
`|AB|=-10` ...
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