Chapter 11.3, Problem 25E

(A) Let $P$ and $Q$ be strategies for the $2\times 2$ matrix game $M$. Let $k$ be a constant, and let $J$ be the matrix with all $1’\text{s}$ as entries. Show that the matrix product $P\left(kJ\right)Q$ equals the $1\times 1$ matrix $k$.

(B) Generalize part (A) to the situation where $M$ and $J$ are $m\times n$ matrix.