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