Show that if A and B are similar, then det A=det B.

Alyce Wilkinson

Alyce Wilkinson

Answered question

2021-11-05

Show that if A and B are similar, then det A=det B.

Answer & Explanation

hajavaF

hajavaF

Skilled2021-11-06Added 90 answers

Consider two similar matrix P and Q
If two matrix are similar, then there wxist a singular matrix A.
Q=A1PA
If P and Q are m×m matrix, then Det(PQ)=Det P * Det Q
DetP=Det(A1QA)
=(DetA1)(DetQ)(DetA)
=(DetQ)(DetA1)(DetA)
=(DetQ)(Det1)
=(Det Q)(Det I)
Det P=Det Q
Results:
Determinant of similar matrices is equal

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