Question

# Find if possible the matrices: a) AB b) BA. A=begin{bmatrix}3 & -2 1 & 5 end{bmatrix} , B=begin{bmatrix}0 & 0 5 & -6 end{bmatrix}

Matrices
Find if possible the matrices:
a) AB b) BA.
$$A=\begin{bmatrix}3 & -2 \\ 1 & 5 \end{bmatrix} , B=\begin{bmatrix}0 & 0 \\ 5 & -6 \end{bmatrix}$$

2021-02-26
Step 1
It is given that,
$$A=\begin{bmatrix}3 & -2 \\ 1 & 5 \end{bmatrix} , B=\begin{bmatrix}0 & 0 \\ 5 & -6 \end{bmatrix}$$
We have to find if possible the matrices:
a) AB b) BA.
Step 2
We have , $$A=\begin{bmatrix}3 & -2 \\ 1 & 5 \end{bmatrix} , B=\begin{bmatrix}0 & 0 \\ 5 & -6 \end{bmatrix}$$
a) AB
$$\Rightarrow AB=\begin{bmatrix}3 & -2 \\ 1 & 5 \end{bmatrix}\cdot \begin{bmatrix}0 & 0 \\ 5 & -6 \end{bmatrix}$$
$$\Rightarrow AB=\begin{bmatrix}3 \times 0 + (-2)5 & 3 \times 0 +(-2)(-6) \\ 1 \times 0 + 5 \times 5 & 1 \times 0 + 5(-6) \end{bmatrix}$$
$$\Rightarrow AB=\begin{bmatrix}-10 & 12 \\ 25 & -30 \end{bmatrix}$$
Hence , $$AB=\begin{bmatrix}-10 & 12 \\ 25 & -30 \end{bmatrix}$$
b) BA
$$\Rightarrow BA=\begin{bmatrix} 0 & 0 \\ 5 & -6 \end{bmatrix}\cdot \begin{bmatrix} 3 & -2 \\ 1 & 5 \end{bmatrix}$$
$$\Rightarrow BA=\begin{bmatrix} 0 \times 3 + 0 \times 1 & 0 \times (-2) +0 \times 5 \\ 5 \times 3 + (-6) \times 1 & 5 \times (-2) + (-6) \times 5 \end{bmatrix}$$
$$\Rightarrow BA=\begin{bmatrix} 0 & 0 \\ 9 & -40 \end{bmatrix}$$
Hence , $$BA=\begin{bmatrix} 0 & 0 \\ 9 & -40 \end{bmatrix}$$