# How do I show that adj(A) is invertible?

• Apr 13th 2010, 10:18 AM
TabishX
How do I show that adj(A) is invertible?
The question I'm working on is basically this:

If A is an invertible nxn matrix, show that adj(A) is also invertible and that:

i've been able to prove their equality..

but i don't know how to approach adj(A) is invertible..

thanks.
• Apr 13th 2010, 10:50 AM
tonio
Quote:

Originally Posted by TabishX
The question I'm working on is basically this:

If A is an invertible nxn matrix, show that adj(A) is also invertible and that:

i've been able to prove their equality..

but i don't know how to approach adj(A) is invertible..

thanks.

What equality were you able to prove?? Perhaps the basic one $\displaystyle A\cdot Adj(A)=\det(A)\cdot I$ ?...but then we're done since:

$\displaystyle \left(A\det(A)^{-1}\right)Adj(A)=I\Longrightarrow$ the matrix $\displaystyle Adj(A)$ is invertible and its inverse is $\displaystyle \left(A\det(A)^{-1}\right)$ ...

Tonio
• Apr 13th 2010, 11:12 AM
TabishX
oh okay.. thank you..