Chapter 16, Problem 3CR

To determine

To find: The correct option for the value of $BA$ .

Answer to Problem 3CR

The correct option is $c$ .

Explanation of Solution

Given information:

The give matrixes are.

  $\begin{array}{l}A=\left[\begin{array}{cc}-2& 3\\ -1& 6\end{array}\right]\\ B=\left[\begin{array}{cc}3& -2\\ -1& 4\end{array}\right]\end{array}$

Calculation:

Calculate the value of $BA$ .

  $\begin{array}{l}BA=\left[\begin{array}{cc}3& -2\\ -1& 4\end{array}\right]\left[\begin{array}{cc}-2& 3\\ -1& 6\end{array}\right]\\ BA=\left[\begin{array}{cc}3\left(-2\right)+\left(-2\right)\left(-1\right)& 3\left(3\right)+\left(-2\right)\left(6\right)\\ \left(-1\right)\left(-2\right)+4\left(-1\right)& \left(-1\right)\left(3\right)+4\left(6\right)\end{array}\right]\\ BA=\left[\begin{array}{cc}-4& -3\\ -2& 21\end{array}\right]\end{array}$

Therefore, the correct option is $c$ .