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 = -3, A₁₂ = 3, A₁₃ = -9, A₂₁ = 0, A₂₂ = -1, A₂₃ = -2, A₃₁ = 0, A₃₂ = 0, A₃₃ = 3.

∴ Adj A =

And |A| = -3.

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