Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: d. Using property c above, show that det Ak = (det A)* for some natural number k. e. Show that det rA = r² det A, for some...

Please include properties and rules for each step.

I need explains for each step

Extracted text: Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: d. Using property c above, show that det Ak = (det A)* for some natural number k. e. Show that det rA = r² det A, for some scalar r.