Q. 2 A5.0( 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 are:

C_{11} = – 3 C_{21} = 2 C_{31} = 2

C_{12} = 2 C_{22} = – 3 C_{23} = 2

C_{13} = 2 C_{23} = 2 C_{33} = – 3

adj A =

=

Now, (adj A).A =

=

=

Also, |A|.I = = ( – 3 + 4 + 4)

=

Then, A.(adj A) =

=

=

Since, (adj A).A = |A|.I = A(adj A)

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