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 = 3 C21 = – 1 C31 = – 1
C12 = – 15 C22 = 7 C32 = – 5
C13 = 4 C23 = – 2 C33 = 2
adj A =
=
adj A =
Now, (adj A).A =
=
=
Also, |A|.I =
= [2(3 – 0) + 0(15 – 0) – 1(5 – 1)]
= (6 – 4)
=
Then, A.(adj A) =
=
=
Hence, (adj A).A = |A|.I = A(adj A)