Partial Solution Set, Leon §4.3 4.3.2 Let

4.3.11 Show that if A and B are similar matrices, then det(A) = det(B).
Solution: If A and B are similar, then B = S −1 AS for some nonsingular S. Now use
the fact that the determinant of a product is the product of the determinants, along with
the commutativity of real multiplication: det B = det(S −1 AS) = det S −1 det A det S =
det S −1 det S det A = det(S −1 S) det A = det I det A = det A.
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