If , find A – 1 and show that A – 1 = 1/2(A2 – 3I).
A = |A| = 0 – 1(0 – 1) + 1(1 – 0) = 0 + 1 + 1 = 2
Cofactors of A are:
C11 = – 1 C21 = 1 C31 = 1
C12 = 1 C22 = – 1 C32 = 1
C13 = 1 C23 = 1 C33 = – 1
adj A =
=
So, adj A =
Now, A – 1 =
A2 – 3I =
=
=
=
Hence, A – 1 = (A2 – 3I)