# Invertible Matrix

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Let   $A$   be a nilpotent matrix. Show that   $I + A$    is invertible.

## Related questions

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Let A be a $5 × 5$ invertible matrix with row sums $1$. That is $\sum_{j=1}^{5} a_{ij} = 1$ for $1 \leq i\leq 5$. Then, what is the sum of all entries of $A^{-1}$.
$1)$ How to find a matrix is diagonalizable or not? Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & -\cos\Theta \end{bmatrix}$ Is it diagonalizable? $2)$ What is it’s eigen spaces?