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

CheemnCatelvew

CheemnCatelvew

Answered question

2021-01-13

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

Answer & Explanation

SchulzD

SchulzD

Skilled2021-01-14Added 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)
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-22Added 2605 answers

Answer is given below (on video)

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