IF `A = [{:( -2,3,-1),( -1,2,-1),( -6,9,-4) :}] and ` `B = [{:( 1,3,-1),( 2,2,-1),( 3,0,-1) :}]` then

Options

A. AB =B'A
B. ` AB ne BA `
C. `AB= 1//2 BA `
D. none of these

Answer

To solve the problem, we will follow these steps:

### Given Matrices:
Let
\[ A = \begin{pmatrix} -2 & 3 & -1 \\ -1 & 2 & -1 \\ -6 & 9 & -4 \end{pmatrix} \]
and
\[ B = \begin{pmatrix} 1 & 3 & -1 \\ 2 & 2 & -1 \\ 3 & 0 & -1 \end{pmatrix} \]

### Step 1: Find \( B^T \) (Transpose of B)
The transpose of a matrix is obtained by swapping its rows and columns.

\[ B^T = \begin{pmatrix} 1 & 2 & 3 \\ 3 & 2 & 0 \\ -1 & -1 & -1 \end{pmatrix} \]