Science:Math Exam Resources/Courses/MATH221/December 2019/Question 03 (d)/Statement

Let $A$ be an $n\times n$ matrix

$$A={\begin{bmatrix}0&1&0&0&\cdots &0&0\\0&0&1&0&\cdots &0&0\\0&0&0&1&\cdots &0&0\\\vdots &\vdots &\vdots &\vdots &\ddots &\vdots &\vdots \\0&0&0&0&\cdots &1&0\\0&0&0&0&\cdots &0&1\\1&0&0&0&\cdots &0&0\end{bmatrix}}$$

Is this matrix invertible? If it is, find the inverse. If it is not, explain why not.