Homework 3 Solutions Math100A UCSD Fall 2001 1. Let a b ; A0 = a0 b0 : c d c0 d0 a Prove by explicit calculation that detAA0 = detA detA0 . b Let A; A0 ; A00 be 2 2 matrices. Prove that AA0 A00 = AA0 A00: This will be an annoying calculation, but at this point there is no other way to prove associativity of 2 2 matrix multiplication than by brute force. In the winter quarter we'll see a more conceptual approach to the issue. c Let A1; : : :; An be 2 2 matrices, with n 2. Prove that detA1 An = detA1 detAn . A= Solution. To standardize our notation, we will write a product of primed and unprimed variables like a0 and a with the unprimed variables coming rst, and in alphabetical order. a By de nitio...
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