Let \(A = \begin{bmatrix}3&-2\\0&5\end{bmatrix}\) and let B be the matrix such that \(A + B = O\), where O is the zero matrix of order 2. Then \(B'\) is equal to
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\begin{bmatrix}-3&0\\2&-5\end{bmatrix}\)
From \(A + B = O\), B is the negative of A: every element of A changes sign.
\( \displaystyle B = -A = \begin{bmatrix}-3&2\\0&-5\end{bmatrix} \)
The transpose turns the rows of B into columns:
\( \displaystyle B' = \begin{bmatrix}-3&0\\2&-5\end{bmatrix} \)