Find the adjoint of the matrix and hence show that A(adj A) = |A| I3.
A =
|A| =
= – 1(1 – 4) + 2(2 + 4) – 2( – 4 – 2)
= 3 + 12 + 12
|A| = 27
Cofactors of A
C11 = – 3 C21 = – 6 C31 = 6
C12 = – 6 C22 = 3 C32 = – 6
C13 = – 6 C23 = – 6 C33 = 3
adj A =
=
So, adj A =
A(adj A) =
=
A(adj A) = 27
Hence, A(adj A) = |A|I