Question

$A=\left[123\right],B=\left[\begin{array}{c}2\\ 3\\ 4\end{array}\right]andc=\left[\begin{array}{cc}1& 5\\ 0& 2\end{array}\right]$ then which of the following is defined

• A. AB
• B. BC
• C. (BA) C
• D. (AC) B

Answer 1

The correct option is A AB

Let's consider two matrices $[X{]}_{n\times m}$ and $[Y{]}_{p\times q}$.

For multiplication of these two matrices $m=p(orq=mforYX)$.

Now, given that

$[B{]}_{3\times 1}$

$[A{]}_{1\times 3}$

$[C{]}_{2\times 2}$

Using the above property only $[AB{]}_{1\times 1}$ is possible.