Compute the determinants using a cofactor expansion across the first row. Also compute the determinant by a cofactor expansion down the second column. [ 0 4 1
5 −3 0
2 3 1 ]

Step-by-step explanation:

Given the 3* 3 matrices , to compute the determinant using the first row means using the row values [0 4 1 ] to compute the determinant. Note that the signs on the values on the first row are +0, -4 and +1

Calculating the determinant;

The determinant is 1 using the first row as co-factor

Similarly, using the second column as the cofactor, the determinant will be expressed as shown;

Note that the signs on the values are -4, +(-3) and -3.

Calculating the determinant;

The determinant is also 1 using the second column as co factor.

It can be concluded that the same value of the determinant will be arrived at no matter the cofactor we choose to use.