Compute the cofactor of the element a12 in the matrix [2 3; 4 5].a.-2b.2c.-4d.4

To compute the cofactor of the element a12 in the matrix [2 3; 4 5], we first need to understand what a cofactor is. In a 2x2 matrix, the cofactor of an element is simply the sign of that element times the element at the opposite corner of the matrix.

The matrix given is:

2 3 4 5

The element a12 is the element in the first row and second column, which is 3.

The element at the opposite corner from a12 is 2.

The sign of a12 is determined by the rule (-1)^(i+j), where i is the row number and j is the column number. For a12, i=1 and j=2, so the sign is (-1)^(1+2) = -1.

Therefore, the cofactor of a12 is -1 * 2 = -2.

So, the correct answer is a. -2.