Question

Find AB if A = \(\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and B = \(\begin{bmatrix}1&5\\3&2\end{bmatrix}\).

(a) AB = \(\begin{bmatrix}15&23\\9&7\end{bmatrix}\)

(b) AB = \(\begin{bmatrix}9&7\\23&15\end{bmatrix}\)

(c) AB = \(\begin{bmatrix}7&9\\15&23\end{bmatrix}\)

(d) AB = \(\begin{bmatrix}7&9\\23&15\end{bmatrix}\)

This question was posed to me during an interview.

This interesting question is from Operations on Matrices topic in chapter Matrices of Mathematics – Class 12

Answer 1

The correct option is (c) AB = \(\begin{bmatrix}7&9\\15&23\end{bmatrix}\)

For explanation I would say: Given that, A = \(\begin{bmatrix}1&2\\3&4\end{bmatrix}\) and B = \(\begin{bmatrix}1&5\\3&2\end{bmatrix}\)

Then, AB = \(\begin{bmatrix}1&2\\3&4\end{bmatrix}\)\(\begin{bmatrix}1&5\\3&2\end{bmatrix}\)

=\(\begin{bmatrix}1×1+2×3&1×5+2×2\\3×1+4×3&3×5+4×2\end{bmatrix}\)=\(\begin{bmatrix}7&9\\15&23\end{bmatrix}\).