CPM Homework Help : A2C Problem 7-221

If $M$ is as shown below, find a matrix $I$ such that $MI = IM = M$ , or write “impossible” and explain why.

$M = \left[ \begin{array} { c c c } { 2 } & { - 1 } & { 5 } \\ { - 4 } & { 0 } & { 7 } \end{array} \right]$
Hint (a):
Notice that this matrix is not a square.

$M = \left[ \begin{array} { c c } { 2 } & { - 1 } \\ { - 4 } & { 0 } \end{array} \right]$
Hint (b):
Remember that there can only be one $1$ in each column and row, and the rest of the numbers are zero.

$M = \left[ \begin{array} { c c c } { 2 } & { - 1 } & { 5 } \\ { - 4 } & { 0 } & { 7 } \\ { 6 } & { - 2 } & { 8 } \end{array} \right]$
Hint (c):
See part (b).