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Let A be a non-singular square matrix. Prove `(A^(-1))^(')=(A^('))^(-1)`

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user6975354 | eNoter

Posted October 3, 2013 at 3:54 AM via web

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Let A be a non-singular square matrix. Prove `(A^(-1))^(')=(A^('))^(-1)`

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aruv | High School Teacher | Valedictorian

Posted October 3, 2013 at 6:08 AM (Answer #1)

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Let  `A^(-1)=B,` by def. of inverse of A

`AB=I` 

Where I and A have same order.

`(AB)'=I'=I`

`(AB)'=I`

`B'A'=I`     (by reversal law)

`B'A'(A')^(-1)=I(A')^(-1)`

`B'=(A')^(-1)`

`Thus`

`(A^(-1))'=(A')^(-1)`

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