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 = -1, A₁₂ = -4, A₁₃ = 1, A₂₁ = 5, A₂₂ = 23, A₂₃ = -11, A₃₁ = 3, A₃₂ = 12, A₃₃ = -6.

∴ Adj A =

= .

And |A| = -3.

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