Inverting Diagonal Matrices

Theorem: Inverting a Diagonal Matrix

A Diagonal Matrix $\mathrm{diag}({\lambda }_1,\cdots ,{\lambda }_n)$ is invertible if and only if none of its diagonal entries are zeroes.

If $\mathrm{diag}({\lambda }_1,\cdots ,{\lambda }_n)$ is invertible, then its inverse is $\mathrm{diag}({\lambda }_1^{-1},\cdots ,{\lambda }_n^{-1})$.

PROOF

TODO