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

1. ## 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.

2. 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 $A\cdot Adj(A)=\det(A)\cdot I$ ?...but then we're done since:

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

Tonio

3. oh okay.. thank you..