Answer to Question #217850 in Linear Algebra for Basil

Question

Let A and B be matrices over R of size n × n. Choose the correct identities

1. A is invertible and λ is an eigenvalue of A, then 1/λ is an eigenvalue of A−1

2. det(λA) = λ det(A), λ ∈ R, λ 6= 0

3. det(Ak) = (det(A))k

4. Let rank(A) = rank(B) = 2, then rank(AB) = 2

5. A and B are invertible, then A + B is invertible