Hi Khaled Megahed ,

I wrote the detail derivation in the picture for you except one or two small steps that I let you to prove them by yourself.

Hope this helps.

MC Trinh

Thank you so much Minh-Chien Trinh

It is well-known Nanson's formula

https://en.wikiversity.org/wiki/Continuum_mechanics/Volume_change_and_area_change

I want to add one more proof, in which the structure of inverse matrix is more clear (to my mind).