Chapter 2.3 Determinants-Properties

Det a proof we have aa1 in consequently 1 det in

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Unformatted text preview: le n × n matrix, then det A−1 = 1 . det A Proof. We have AA−1 = In . Consequently, 1 = det In = det(AA−1 ) = (det A)(det A−1 ) Therefore det A−1 = 1 . det A Outline Linearity of the Determinant Determinants and Invertibility Determinants and Products Determinants and Inverses Example Example 1 If A is invertible, and det A = −7, what is det(A−1 (AT )−1 )? 2 If det A = 2 and det B = −3, what is det(AB )−1 ? 3 An orthogonal matrix is an invertible matrix such that A−1 = AT . What is the determinant of an orthogonal matrix?...
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