Chapter 2.4, Problem 7E

In Exercises 5–8, find formulas for X, Y, and Z in terms of A, B and C, and justify your calculations. In some cases, you may need to make assumptions about the size of a matrix in order to produce a formula. [Hint: Compute the product on the left, and set it equal to the right side.]

7. $\left[\begin{array}{ccc}X& 0& 0\\ Y& 0& I\end{array}\right]\left[\begin{array}{cc}A& Z\\ 0& 0\\ B& I\end{array}\right]=\left[\begin{array}{cc}I& 0\\ 0& I\end{array}\right]$