Matrices and determinant properties?

[maiad]

Homework Statement

Homework Equations

The Attempt at a Solution

I tried to see if the problem has any properties with determinants that i can apply but the properties i learned didn't involve the use of adjoint matrices so I'm kind of stumped on this one.
Any hints would be grateful. Thank you in advance

 

[DryRun]

Your classmate asked the same question, which i already replied to in this topic:
https://www.physicsforums.com/showthread.php?t=596508