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).

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)

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

step-by-step explanation: