Answer :

We know that

Adjoint of the matrix A = [a_{ij}]_{n×n} is defined as the transpose of the matrix [A_{ij}]_{n×n} where A_{ij} is the co-factor of the element a_{ij}.

Let’s find the cofactors for all the positions first-

Here, A_{11} = 2, A_{12} = 3, A_{21} = -5, A_{22} = -1.

∴ Adj A =

=

And |A| = -1(2)-(-3)(5) = 13

So

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