Question

设A是三阶矩阵,其行列式|A|=5 求出行列式|(5A*)-1|的值

Answer 1

|(5A*)^-1|

= 1/ |5A*|

= 1/ ( 5^3 |A*|)

= 1/ (5^3 * 5^2)

= 1/5^5.

知识点:|A*| = |A|^(n-1)

|A^-1| = 1/|A|