Question

The trace of an n×n matrix A, denoted tr(A), is thesum of its diagonal entries; that is,tr(A) = a11 + a22 +· · ·+annShow that(a) tr(AB) = tr(BA)(b) if A is similar to B, then tr(A) = tr(B).

Answer 1

Answer:

Step-by-step explanation:

for two matrices A, B to be Similar, then A = SBS⁻¹

A=SBS−1⟹trace(A)=trace((SB)(S−1))=trace((S−1)(SB))=trace((SS−1)B)=trace(B)