Question

If matrix A=\(\begin{bmatrix}4&1\\6&2\end{bmatrix}\)  and B=\(\begin{bmatrix}-1&3\\2&1\\6&6\end{bmatrix}\), then find A’ B’.

(a) \(\begin{bmatrix}14&14\\5&4\\6&18\end{bmatrix}\)

(b) \(\begin{bmatrix}14&5\\14&4\\6&18\end{bmatrix}\)

(c) \(\begin{bmatrix}14&14&60\\5&4&18\end{bmatrix}\)

(d) \(\begin{bmatrix}14&14&18\\5&4&60\end{bmatrix}\)

I have been asked this question in an online quiz.

The question is from Transpose of a Matrix topic in division Matrices of Mathematics – Class 12

Answer 1

The correct choice is (c) \(\begin{bmatrix}14&14&60\\5&4&18\end{bmatrix}\)

For explanation I would say: Given that, A=\(\begin{bmatrix}4&1\\6&2\end{bmatrix}\)  and B=\(\begin{bmatrix}-1&3\\2&1\\6&6\end{bmatrix}\)

⇒A’=\(\begin{bmatrix}4&6\\1&2\end{bmatrix}\)  and B’=\(\begin{bmatrix}-1&2&6\\3&1&6\end{bmatrix}\)

⇒A’ B’=\(\begin{bmatrix}4&6\\1&2\end{bmatrix}\)\(\begin{bmatrix}-1&2&6\\3&1&6\end{bmatrix}\)=\(\begin{bmatrix}14&14&60\\5&4&18\end{bmatrix}\).