The determinant of a matrix is scaled by the factor of the scalar raised to the power of the size of the matrix. That is, for a matrix A, and a scalar k, |kA|=kn|A|, where n is the order of the matrix. In this case, n=3, so: |5A|=53|A|=125|A| Quick Tip When multiplying a matrix by a scalar, the determinant is multiplied by the scalar raised to the power of the matrix's order.