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 = 0, A₁₃ = 0, A₂₁ = 0, A₂₂ = -cosα, A₂₃ = -sinα, A₃₁ = 0, A₃₂ = -sinα, A₃₃ = cosα.

∴ Adj A =

And |A| = 1.

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