Q. 93.7( 18 Votes )

# Find the inverse of each of the matrices (if it exists)

Answer :

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} = -1, A_{12} = -4, A_{13} = 1, A_{21} = 5, A_{22} = 23, A_{23} = -11, A_{31} = 3, A_{32} = 12, A_{33} = -6.

∴ Adj A =

= .

And |A| = -3.

.

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