Quiz 3, 4/13/2006, Math 221, s. 02

Suppose the 2 × 2 matrix A = [	a   b	] is invertible and satisfies:
	c   d

A A = I_{2 × 2} ,
A = A^T , and  
det(A) < 0 .  

Prove:

(a) b = c ;
(b) a² + b² = 1 ;
(c) det(A) = – 1 ; and
(d) d = – a .

Please do not consult outside sources (books, notes, web, people) while working out this quiz.
Please do record the clock times at which you begin and end work on this quiz.
(The most likely expectation is a total elapsed time of not more than 15 minutes.)
And please do observe — and indicate your observance of — the Wesleyan Honor Code.

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First posted: 16 Apr 2006.

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Contents © 2006 by Fred E.J. Linton