If \( A=\begin{bmatrix} 2 & -1 & 3\\ 4 & 5 & -6\end{bmatrix} \) and \( B=\begin{bmatrix} 1 & 2\\ 3 & 4\\ 5 & -6\end{bmatrix} \) then
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( AB \) and \( BA \) are both defined
A is of order \( 2\times 3 \) and B is of order \( 3\times 2 \). A product is defined when the columns of the first equal the rows of the second.
AB is defined, since A has 3 columns and B has 3 rows. It is \( 2\times 2 \).
BA is defined, since B has 2 columns and A has 2 rows. It is \( 3\times 3 \).