If \(A = \begin{bmatrix}-3&8\\4&-2\end{bmatrix}\) and \(B = \begin{bmatrix}x&y\\z&w\end{bmatrix}\) are such that \(A + B = I\), where I is the identity matrix of order 2, then which of the following is NOT true?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(z = 4\)
From \(A + B = I\),
\( \displaystyle B = I - A = \begin{bmatrix}1 - (-3)&0 - 8\\0 - 4&1 - (-2)\end{bmatrix} \)
\( \displaystyle B = \begin{bmatrix}4&-8\\-4&3\end{bmatrix} \)
By equality of matrices, \(x = 4\), \(y = -8\), \(z = -4\) and \(w = 3\).
So \(z = 4\) is not true, since \(z = -4\).