If \(A^T =\begin{bmatrix}-2&3\\1&2\end{bmatrix}\), and \(B =\begin{bmatrix}-1&0\\1&2\end{bmatrix}\), then the matrix \((A + 2B)^T\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\begin{bmatrix}-4&5\\1&6\end{bmatrix}\)
Since the transpose of a sum is the sum of the transposes, \(A^T\) can be used as given, without finding A:
\((A + 2B)^T = A^T + 2B^T\)
\( \displaystyle B^T = \begin{bmatrix}-1&1\\0&2\end{bmatrix},\quad 2B^T = \begin{bmatrix}-2&2\\0&4\end{bmatrix} \)
\( \displaystyle (A + 2B)^T = \begin{bmatrix}-2&3\\1&2\end{bmatrix} + \begin{bmatrix}-2&2\\0&4\end{bmatrix} \)
\( \displaystyle (A + 2B)^T = \begin{bmatrix}-4&5\\1&6\end{bmatrix} \)
NCERT (2026-27 edition):
Transpose of a Matrix
