设A为三阶矩阵,且|A|=-3,则|-3A|的值是多少

题目

设A为三阶矩阵,且|A|=-3,则|-3A|的值是多少

答案

|-3A|
= (-3)^3 |A| --- |kA| = k^n|A|
= (-3)^3 * (-3)
= 81.