Two n × n square matrices A and B are said to be similar if there exists a non-singular matrix P such that P–1A P = B. If A and B are two similar matrices, then

Engineering

Mathematics

Introduction to Determinants

Question

Two n × n square matrices A and B are said to be similar if there exists a non-singular matrix P such that P^–1A P = B. If A and B are two similar matrices, then

det(A) = det(B)

det(A) + det(B) = 0

det(AB) ≠ 0

none of these

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As A and B are similar matrices there exists a non-singular matrix P such that A = P^–1 BP

⇒ det(A) = det(P^–1 BP)

= det(P^–1) det(B) det(P)

= \frac{1}{\det (P)} \det (B) (detP)

= det B
Hence, option A.

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