If , show that A – 1 = A3.
A =
|A| = 3 + 6 – 8 = 1
Cofactors of A are:
C11 = 1 C21 = – 1 C31 = 0
C12 = – 2 C22 = 3 C32 = – 4
C13 = – 2 C23 = 3 C33 = – 3
adj A =
=
So, adj A =
Now, A – 1 =
Also, A2 =
A3 = A2.A =
Hence, A – 1 = A3