# Endomorphism/Simple properties of invariant subspaces/Exercise

Let a linear mapping on a -vector space over a field . Show the following properties.

- The zero space is -invariant.
- is -invariant.
- Eigenspaces are -invariant.
- Let be -invariant linear subspaces. Then also and are -invariant.
- Let be a -invariant linear subspace. Then also the image space and the preimage space are -invariant.