Let A and B be two invertible matrices of order 3 [ ] 3.

Question

Let A and B be two invertible matrices of order 3 $$ \times $$ 3. If det(ABAT) = 8 and det(AB--1) = 8,

then det (BA--1 BT) is equal to :

Accepted Answer

$${\left| A \right|^2}.\left| B \right| = 8$$

and  $${{\left| A \right|} \over {\left| B \right|}} = 8 \Rightarrow \left| A \right| = 4$$

and $$\left| B \right| = {1 \over 2}$$

$$ \therefore $$  det(BA-1. BT)  $$ = {1 \over 4} \times {1 \over 4} = {1 \over {16}}$$

Solutions · 1