If A and B are similar matrices such that det(AB) = 0, then

Engineering

Mathematics

Special Type of Square Matrices

Properties of Determinant

Question

If A and B are similar matrices such that det(AB) = 0, then

A = 0 and B = 0

det(A) = 0 and det(B) = 0

A = 0 or B = 0

det(A) = 0 and det(B) ≠ 0

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Given. two n × n square matrices A and B

Given, B = P^–¹AP

det⁡(B) = det⁡(P^–¹AP)

det⁡(B) = (det⁡(P))^–¹(det⁡(A))(det⁡(P))

det⁡(B) = det⁡(A)

det⁡(AB) = (det⁡(A))(det⁡(B))

If (det⁡(A)) = 0 then (det⁡(B)) also zero.