If A is a $4 \times 4$ matrix with integer entries, the cofactor of each element is an integer.

Question

Quizplus · Accepted Answer

The cofactor of an element in a matrix is the determinant of the submatrix obtained by removing the row and column containing that element, multiplied by -1 raised to the power of the sum of the row and column indices of that element. Since the determinant of a matrix with integer entries can be computed using integer operations, and the power of -1 is either 1 or -1 (which are both integers), it follows that the cofactor of each element in a matrix with integer entries is an integer.

If a Is A 4×44 \times 44×4 Matrix with Integer Entries, the Cofactor of Each Element Is

If a Is A $4 \times 4$ Matrix with Integer Entries, the Cofactor of Each Element Is