A =

Cofactors of A are

C₁₁ = d

C₁₂ = – c

C₂₁ = – b

C₂₂ = a

Since, adj A =

(adj A) =

=

Now, (adj A)A =

(adj A)A =

And, |A|.I =

Also, A(adj A) =

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