Q. 2 D5.0( 1 Vote )

# 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.

Answer :

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)

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