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## Main Question or Discussion Point

What exactly is the relationship between the trace/determinant of two matrices with regards to similarity. I always thought that if the trace was the same, then there is a possibility that the matrices are similar and if the determinant was the same, then the matrices are similar. On a recent exam we were given three matrices

A

1 0 1

2 3 5

0 2 -6

B

-4 3 4

0 1 2

0 0 1

C

0 0 2

0 4 1

3 5 -2

One of these matrices is similar to A.

I found det(a) = det (c) but trace (a) is not equal to trace (c). Det(B) is not equal to det (a) but trace (a) = Trace (b). Do I have my facts wrong?

A

1 0 1

2 3 5

0 2 -6

B

-4 3 4

0 1 2

0 0 1

C

0 0 2

0 4 1

3 5 -2

One of these matrices is similar to A.

I found det(a) = det (c) but trace (a) is not equal to trace (c). Det(B) is not equal to det (a) but trace (a) = Trace (b). Do I have my facts wrong?