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{(3×1-0×5)} = 3

Similarly,

A₁₂ = -12, A₁₃ = 6, A₂₁ = 1, A₂₂ = 5, A₂₃ = 2, A₃₁ = -11, A₃₂ = -1, A₃₃ = 5.