Give an example of a non-zero 2 × 2 matrix R which satisfics R² = 0. Suppose that M is an n x n matrix satisfying M³ = 0. Show that (I – M)-1 (I+M + M²). Since R2 = 0 implies R* = 0, use the previous part to find the inverse of (I – R).

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I bought a new gas lawn mower the other day. This new mower mows faster than the old electric (environmental) one. Why, you ask? It is because the old mower cut a 21 inch path, while the new one cuts a 22 inch path. So how much time did I save? Look at some facts. My lawn is a rectangle measuring 150 feet by 105 feet I mow the lawn in strips and always in the same direction (length or width) My walking speed is 120 feet/minute It takes 5 seconds to turn around after each strip How much time did I save if I mow back and forth along the width or if I mow back and forth along the length? Pick one and figure it out. My neighbor does not like minutes the noise it makes, but I do!

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I'm confused on how to do the second part of the problem still.