Compute the cofactor of the element a21 in the matrix [1 2; 3 4].a.2b.1c.-1d.-2

The cofactor of an element in a matrix is calculated by removing the row and column of that element, finding the determinant of the resulting 1x1 matrix, and then multiplying by (-1)^(i+j), where i and j are the row and column numbers of the element.

Here, the element a21 is 3. It's in the 2nd row and 1st column.

After removing the 2nd row and 1st column, we're left with a 1x1 matrix: [2].

The determinant of a 1x1 matrix is just the element itself, so the determinant is 2.

Then, we multiply by (-1)^(2+1) = -1.

So, the cofactor of a21 is -1 * 2 = -2.

Therefore, the correct answer is (d) -2.