Question

Let M and J be two nxn matrices such that

JMJ-1=
0 1 0 0
0 0 2 0
0 0 0 1
4 0 0 0
Compute the determinant of M.

Answer 1

-8

Explanation:

Answer 2

-8

Explanation:

The determinant of the given matrix is the determinant of M.

It is convenient to find the cofactor of the value 4. It is the opposite of the determinant of the diagonal matrix

`\left[\begin{array}{ccc}1&0&0\\0&2&0\\0&0&1\end{array}\right]`

whose determinant is the product of the diagonal elements.

Since all the other elements of row 4 of the given matrix are zero, the determinant of M is the product of 4 and -2:

4(-2) = -8