Question

Find integer matrices such that (1) neither of them are diagonal matrices, and (2) ________.

1) They have the same determinant
2) They have the same trace
3) They have the same eigenvalues
4) They have the same rank

Answer 1

To find integer matrices that (1) are not diagonal matrices and (2) have the same determinant, you can consider the example provided.

Step-by-step explanation:

To find integer matrices that (1) are not diagonal matrices and (2) have the same determinant, we can consider the following example:

Let matrix A be:

A = [1 2; 2 4]

The determinant of matrix A is (1 × 4) - (2 × 2) = 0.

Now, let matrix B be:

B = [-4 -2; -2 -1]

The determinant of matrix B is (-4 × -1) - (-2 × -2) = 0.

Both matrices A and B are not diagonal matrices, and they have the same determinant.