### Home > A2C > Chapter 7 > Lesson 7.3.5 > Problem7-221

7-221.

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

1. $M = \left[ \begin{array} { c c c } { 2 } & { - 1 } & { 5 } \\ { - 4 } & { 0 } & { 7 } \end{array} \right]$

Notice that this matrix is not a square.

1. $M = \left[ \begin{array} { c c } { 2 } & { - 1 } \\ { - 4 } & { 0 } \end{array} \right]$

Remember that there can only be one $1$ in each column and row, and the rest of the numbers are zero.

1. $M = \left[ \begin{array} { c c c } { 2 } & { - 1 } & { 5 } \\ { - 4 } & { 0 } & { 7 } \\ { 6 } & { - 2 } & { 8 } \end{array} \right]$

See part (b).