If A is a square matrix such that |A|= 2 then find the valu of |AA(transpose)|

Question

It is a question from previous year maths paper....i found it confusing....so need help

 

Answer 1

I assume that |A| = 2 means that the determinant of A is 2.

 

|AA^t| = ?

 

Use the following two properties of determinants (I will not prove them, but you can find them in a basic linear algebra text book):

 

|A^t| = |A|

 

|AB| = |A||B|

 

Then 

 

|AA^t| = |A||A^t| = |A|² = 2² = 4