(vii) If P is a invertible square matrix, then

• (P^T)^–1 = (P^–1)^T
• (P^k)^–1 = (P^–1)^k, k ∈ N
• adj(A^–1) = (adj A)^–1

(viii) P = diag(a1, a2, a3......an)

⇒ P^–1 = diag(a^–1₁, a^–1₂, a^–1₃......a^–1_n).

(ix) Inverse of a diagonal matrix is also diagonal.

(x) Inverse of a triangular matrix is also triangular.

(xi) Inverse of a scalar matrix is also a scalar matrix.

(xii) Every invertible matrix possesses a unique inverse.