Question

 If  \[A = \begin{bmatrix}2 & 1 & 4 \\ 4 & 1 & 5\end{bmatrix}and B = \begin{bmatrix}3 & - 1 \\ 2 & 2 \\ 1 & 3\end{bmatrix}\] . Write the orders of AB and BA.

 

 

Answer 1

The order of matrix A is

\[2 \times 3\]  and the order of matrix B is

\[3 \times 2\]

Since the number of columns in A is equal to the number of rows in B, AB exists and it is of order

\[2 \times 2\]

Also, since the number of columns in B is equal to the number of rows in A, BA exists and it is of order

\[3 \times 3\]