Unformatted text preview: le n × n matrix, then
det A−1 = 1
det A Proof.
We have AA−1 = In .
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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