Inverse of Matrix

samsam

New member
Joined
Mar 30, 2015
Messages
1
If A is an invertible nxn matrix, Prove A2 is also invertible.


I have tried by just using algebra definitions using the identity matrix, but can't quite seem to follow the right path.
 
If A is an invertible nxn matrix, Prove A2 is also invertible.


I have tried by just using algebra definitions using the identity matrix, but can't quite seem to follow the right path.
We can show the inverse to A2 exists if we can find a matrix to multiply it by to get the identity matrix.

Let
A2 = B
Since we know A-1 exists, what would happen if we multiplied through by that? And then that again?
 
We can show the inverse to A2 exists if we can find a matrix to multiply it by to get the identity matrix.

Let
A2 = B
Since we know A-1 exists, what would happen if we multiplied through by that? And then that again?


Seems to be a fairly easy problem.Use the basic determinants properties.If A-1 exists then det(A)!=0 then det(A2)=[det(A)]2 ​>0
 
Last edited:
Top