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

Question

Philoid · Accepted 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, A₁₁ = 2, A₁₂ = -9, A₁₃ = -6, A₂₁ = 0, A₂₂ = -2, A₂₃ = -1, A₃₁ = -1, A₃₂ = 3, A₃₃ = 2.

∴ Adj A =

=

And |A| = -1.