We have,

To show: A^-1 = A²

Firstly, we have to find A^-1 and

Calculating |A|

Expanding |A| along C₁, we get

= 1(0) – 2(0) + 1(0 – (-1))

= 1(1)

= 1

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

…(i)

Calculating A²

= A^-1 [from eq. (i)]

Thus, A² = A^-1

Hence Proved