设3阶方阵A的行列式的值是2,则(2/3A)的逆的行列式是什么,要具体解

Question

如题所述

Answer 1

知识点:
|kA| = k^n |A|
|A^-1| = |A|^-1.
(kA)^-1 = (1/k)A^-1
|((2/3)A)^-1|
= | (3/2) A^-1|
= (3/2)^3 |A^-1|
= (3/2)^3 (1/2)
= 27/16.