A and B are n×n matrices. Check the true statements below: A. (detA)(detB)=detAB. B. The determinant of A is the product of the diagonal entries in A. C. If λ+5 is a factor of the characteristic polynomial of A, then 5 is an eigenvalue of A. D. An elementary row operation on A does not change the determinant.
1 answer:
Answer with Step-by-step explanation:
We are given that
A and B are matrix.
A.We know that for two square matrix A and B
Then,
Therefore, it is true.
B. det A is the product of diagonal entries in A.
It is not true for all matrix.It is true for upper triangular matrix.
Hence, it is false.
C.
When is a factor of the characteristics polynomial of A then -5 is an eigenvalue of A not 5.
Hence, it is false.
D.An elementary row operation on A does not change the determinant.
It is true because when an elementary operation applied then the value of matrix A does not change.
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