Black's Theorem

Black's Theorem, a key concept in linear algebra, describes how the determinant of a product of two matrices relates to the determinants of the individual matrices. Specifically, it states that the determinant of the product equals the product of the determinants: \(\det(AB) = \det(A) \times \det(B)\). This property helps us understand how transformations combine: if each matrix represents a change of space, their combined effect's size distortion (measured by determinants) is simply the product of their individual effects. This makes calculations more manageable and provides insight into the nature of linear transformations.