Use an Inverse Matrix to Find the Solution to the System

Multiple Choice

Use an inverse matrix to find the solution to the system.
-Two phone companies compete for customers in a city. Company 1 retains $3 / 4$ of its customers and loses $1 / 4$ of its customers to Company 2. Company 2 retains $5 / 6$ of its customers and loses $1 / 6$ to Company 1 . If we represent the fraction of the market held last year by $\left[ \begin{array} { l } a \\ b \end{array} \right]$ , where $a$ is the number the that Company 1 had last year and $b$ is number that Company 2 had last year, then the number that each company will have this year can be found by tl following matrix equation.
$$\left[ \begin{array} { l } \mathrm { A } \\\mathrm { B }\end{array} \right] = \left[ \begin{array} { l l } 3 / 4 & 1 / 6 \\1 / 4 & 5 / 6\end{array} \right] \left[ \begin{array} { l } \mathrm { a } \\\mathrm { b }\end{array} \right]$$
If Company 1 has $\mathrm { A } = 81,000$ customers and Company 2 has $\mathrm { B } = 153,000$ customers this year, then how many customers did Company 2 have last year?

A) 162,000 customers
B) 76,000 customers
C) 72,000 customers
D) 168,000 customers