Q. 385.0( 2 Votes )

Find the adjoint of the matrix and hence show that A(adj A) = |A| I3.

Answer :

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


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