Question

If  \[A = \begin{bmatrix}2 & - 1 & 3 \\ - 4 & 5 & 1\end{bmatrix}\text{ and B }= \begin{bmatrix}2 & 3 \\ 4 & - 2 \\ 1 & 5\end{bmatrix}\] then

Options

• only AB is defined

• only BA is defined

• AB and BA both are defined

• AB and BA both are not defined

Answer 1

Given : 

\[A = \begin{bmatrix}2 & - 1 & 3 \\ - 4 & 5 & 1\end{bmatrix} \text{and B }= \begin{bmatrix}2 & 3 \\ 4 & - 2 \\ 1 & 5\end{bmatrix}\]

Order of A is 2 × 3 and order of B is 3 × 2.

Therefore, AB and BA both are defined.

Hence, the correct option is (c).