True or False - Determinants of two similar matrices are the same. Explain.

CheemnCatelvew 2021-01-13 Answered
True or False - Determinants of two similar matrices are the same. Explain.
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Expert Answer

SchulzD
Answered 2021-01-14 Author has 83 answers
Step 1
According to the given information, it is required to say whether the given statement is true or not.
The given statement is true as if two matrices are similar then their determinant are equal.
Step 2
Let A and B are similar matrices.
When two matrices are similar then there exists a non-singular matrix such that: let the non singular matrix be L then ,
L1AL=B
take determinant both sides
det(L1AL)=det(B)
det(L1AL)=det(B)
det(L1)det(A)det(L)=det(B)[ as det (AB)=det(A)det(B)]
det(L1)det(L)det(A)=det(B)[ determinant of any matrix is a number so it is commutative ]
det(L1L)det(A)=det(B)
det(I)det(A)=det(B)[det(I)=1]
det(A)=det(B)
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Jeffrey Jordon
Answered 2022-01-22 Author has 2262 answers

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