Question: Prove that each statement holds for 2 2 matrices. (a) The determinant of a product is the product of the determinants det(ST) = det(S)

Prove that each statement holds for 2 × 2 matrices.
(a) The determinant of a product is the product of the determinants det(ST) = det(S) ∙ det(T).
(b) If T is invertible then the determinant of the inverse is the inverse of the determinant det(T-1) = (det(T))-1.
Matrices T and T′ are similar if there is a nonsingular matrix P such that T′ = PTP-1. Show that similar 2 × 2 matrices have the same determinant.

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a Plug and chug the determinant of the product is this acwx adwz bcxy bdyz ... View full answer

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