The product of all eigenvalues of the matrix

| 1 2 3 |
| 4 5 6 |
| 7 8 9 |

is

A. -1
B. 0
C. 1
D. 2

Question

The product of all eigenvalues of the matrix

| 1  2  3 |
    | 4  5  6 |
    | 7  8  9 |

is

A. -1
B. 0
C. 1
D. 2

Accepted Answer

Product of all eigenvalues = det(M) = 0. Answer: B The product of all eigenvalues of a matrix equals its determinant. If any eigenvalue is 0, the determinant is 0. For this matrix, the third row equals the second row minus the first row multiplied by appropriate factor, making the rows linearly dependent and the determinant zero.

The product of all eigenvalues of the matrix | 1 2 3 | | 4 5 6 | | 7 8 9 | is A. -1 B. 0 C. 1 D. 2