Question

IF $A=\left[\begin{array}{ccc}-1& 0& 2\\ 3& 1& 2\end{array}\right]$ and $B=\left[\begin{array}{cc}-1& 5\\ 2& 7\\ 3& 10\end{array}\right],$ then

• A. $AB$ and $BA$ both exist
• B. $AB$ exists but bot $BA$
• C. $BA$ exists but not $AB$
• D. but $AB$ and $BA$ do not exist

Answer 1

The correct option is A $AB$ and $BA$ both exist

Since, order of $A$ is $2\times 3$ and order of $B$ is $3\times 2$
Thus, $AB$ and $BA$ exists.