Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: a. If you exchange two rows of A to produce matrix B, then det(A) = -det(B). b. det AT = det A c. JAC| = |A||C|

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: a. If you exchange two rows of A to produce matrix B, then det(A) = -det(B). b. det AT = det A c. JAC| = |A||C|