Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
A =
Cofactors of A
C11 = 2 C21 = 3 C31 = – 13
C12 = – 3 C22 = 6 C32 = 9
C13 = 5 C23 = – 3 C33 = – 1
adj A =
=
adj A =
Now, (adj A).A =
=
=
Also, |A|.I = = [1(3 – 1) – 2(2 + 1) + 5(2 + 3)]
= (21)
=
Then, A.(adj A) =
=
=
Hence, (adj A).A = |A|.I = A(adj A)