Question

1. If A is an invertible matrix, then what is det(A-1) equal to?

a) 0
b) det (A)
c) 1/det(A)
d) 1
​

Answer 1

b) det (A)

Explanation:

The determinant of the inverse of an invertible matrix is the inverse of the determinant: det(A-1) = 1 / det(A) [6.2. 6, page 265]. Similar matrices have the same determinant; that is, if S is invertible and of the same size as A then det(S A S-1) = det(A).

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