**Unformatted text preview: **F n and A is the matrix of T in this ordered basis, show that det A = c . (d) What is a reasonable name for the scalar c 6 If A is n × n over C for odd n , and A T =-A , i.e. A is skew symmetric, then show det A = 0. 6 If A is orthogonal show det A = ± 1. 6 Let A be n × n over C and suppose that it is unitary, i.e. AA * = I n . Show that | det( A ) | = 1. 6 Let A ∈ F n × n . Prove that there are at most n distinct scalars c in F such that det( cI-A ) = 0 . 6 Let A and B be n × n over F . Show that if A is invertible there are at most n scalars c such that cA + B is not invertible. 1...

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