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

aruv | Student

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)`