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Chapter 6: Q59E (page 293)

If the equationdetA=detBholds for two n x n matrices A and B , is A necessarily similar to B?

Short Answer

Expert verified

Therefore, A and B are not similar.

Step by step solution

01

Matrix Definition 

Matrix is a set of numbers arranged in rows andcolumns so as to form a rectangular array.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be a 鈥� m by n鈥� matrix, written 鈥� mxn.鈥�

02

To find if A is similar to B

Letn=2,A=4001B=2002Clearly,detA=detB=4.Assume,AandBaresimilar.Then,鈭�T鈭�鈩�2x2,T-1AT=BA=TBT-1A=2TIT-1A=2IA鈮�A.Wegotacontradiction.So,AandBarenotsimilar.

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