We have,

To show: A^-1 = A’

Firstly, we find the Transpose of A, i.e. A.’

Here,

So, …(i)

Now, we have to find A^-1 and

Calculating |A|

Expanding |A| along C₁, we get

= -1

Now, we have to find adj A, and for that, we have to find co-factors:

= A’ [from eq. (i)]

Thus, A^-1 = A’

Hence Proved