Question

If a non-singular matrix of order 3 and |A^-1|=|A|^k, then find the value of k

Answer 1

Answer : K = - 1 .

We know that , 

A.A^-1 = I_3×3 

_{\(\therefore\)}  | A.A^-1| = | I | = 1 

\(\therefore\) | A |.|A^-1| = 1 

\(\therefore\) | A^-1 | = 1/ | A | 

\(\therefore\) | A^-1 | = | A |^-1 

\(\therefore\)  k = - 1