If \(A = \begin{bmatrix}1&2\\-1&3\end{bmatrix}\), \(B = \begin{bmatrix}x&4\\-2&5\end{bmatrix}\) and \(AB = BA\), then the value of \(x\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1
Multiplying row by column:
\( \displaystyle AB = \begin{bmatrix}x - 4&4 + 10\\-x - 6&-4 + 15\end{bmatrix} = \begin{bmatrix}x - 4&14\\-x - 6&11\end{bmatrix} \)
\( \displaystyle BA = \begin{bmatrix}x - 4&2x + 12\\-2 - 5&-4 + 15\end{bmatrix} = \begin{bmatrix}x - 4&2x + 12\\-7&11\end{bmatrix} \)
By equality of matrices, the elements in the first row, second column give
\(2x + 12 = 14\)
\(x = 1\)
The second row, first column agrees: \(-1 - 6 = -7\).