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