MHB Is A Invertible When Each Diagonal Element is Nonzero?

[karush]

$\textsf{Let }$
$A=\textit{diag} (a_1,a_2,...,a_n)$.
$\textsf{Show that A is invertible iff each}$
$a_i\ne 0.$

$\textsf{Ok I didn't know formally how to answer this.}$
$\textsf{Except i can see that an $a=0$ would mess things up}$

 

[Greg]

I don't know if this helps but a matrix is invertible iff its determinant is non-zero.

 

[HOI]

The inverse matrix for the diagonal matrix with a_1, a_2, … , a_n on the diagonal, is, rather trivially, the diagonal matrix with 1/a_1, 1/a_2, …, 1/a_n on the diagonal. Show that and you are finished.