If A = , prove that A^-1 = A³.

We have,

To show: A^-1 = A³

Firstly, we have to find A^-1 and

Calculating |A|

Expanding |A| along C₁, we get

= 3(-3 – (-4)) – 2(-3 – (-4)) + 0

= 3(- 3 + 4) – 2(-3 + 4)

= 3(1) – 2(1)

= 3 – 2

= 1

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

…(i)

Calculating A³

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

Thus, A³ = A^-1

Hence Proved