Contents 
Let and be two second order tensors. Show that
Proof:
Using index notation,
Hence,
Let be a second order tensor and let and be two vectors. Show that
Proof:
It is convenient to use index notation for this. We have
Hence,
Let and be two second order tensors and let and be two vectors. Show that
Proof:
Using index notation,
Hence,
Let be a second order tensors and let and be two vectors. Show that
Proof:
For the first identity, using index notation, we have
Hence,
For the second identity, we have
Therefore,
Now, and . Hence,
Therefore,
