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 = 10, A₁₂ = 0, A₁₃ = 0, A₂₁ = -10, A₂₂ = 5, A₂₃ = 0, A₃₁ = 2, A₃₂ = -4, A₃₃ = 2.

∴ Adj A =

And |A| = 10.