If \( \mathrm{A}=\begin{bmatrix}1 & 2 & 3\\4 & 5 & 6\end{bmatrix} \) and \( \mathrm{B}=\begin{bmatrix}1 & 2\\3 & 4\\5 & 6\end{bmatrix} \), then \( \mathrm{A+B} \) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → not defined
Two matrices can be added only when they have the same order.
A has 2 rows and 3 columns (order 2 × 3), while B has 3 rows and 2 columns (order 3 × 2).
The orders are different, so A + B is not defined.
Why the other options are incorrect
Option (1) \( \begin{bmatrix}1 & 4 & 6\\8 & 10 & 12\end{bmatrix} \) — Incorrect. The orders of A and B differ, so no matrix can be A + B.
Option (2) \( \begin{bmatrix}1 & 4\\6 & 8\\10 & 12\end{bmatrix} \) — Incorrect. For the same reason, no 3 × 2 matrix can be A + B.
Option (3) \( \begin{bmatrix}22 & 28\\49 & 64\end{bmatrix} \) — Incorrect. This is the product AB (a 2 × 3 matrix times a 3 × 2 matrix gives a 2 × 2 matrix); the product is defined, but the sum is not.