2x2-matrix/At least one 0/Not two 0/Exercise

Let

${}M={\begin{pmatrix}a&b\\c&d\end{pmatrix}}\,$

be a matrix over a field ${}K$.

a) Show that there exists a matrix that is similar to ${}M$, and where at least one entry equals ${}0$.

b) Show that, in general, there does not exist a matrix that is similar to ${}M$, and where at least two entries equal ${}0$.

Create a solution