27. Let n be an odd number and A be an n × n real matrix....

Question

Question

27. Let n be an odd number and A be an n x n real matrix. If A is orthogonal, i.e., AT A = 13, and det(A) = 1, show that 1 is

27. Let n be an odd number and A be an n × n real matrix. If A is orthogonal, i.e., ATA = I3, and det(A) = 1, show that 1 is an eigenvalue of A.

Answer 1

Answer #1

(: detA =1) det ( I-A) = det A. det (I-A) det (AT). det (I-A) (: det AT= detA) det (AT I- ATA) dit AT- I). = del CA-1)) det (

Answer 2

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