Question

Let \( A = \begin{bmatrix} 0 & -3 & 4 \\ 1 & 0 & 2 \end{bmatrix} \) and \( B = \begin{bmatrix} -3 & 0 & 1\\ 2 & 4 & 0 \end{bmatrix} \). If \( A + B + C = O \), then matrix \( C \) is :

• A. \( \begin{bmatrix} -3 & -3 & 5\\ 3 & 4 & 2 \end{bmatrix} \)
• B. \( \begin{bmatrix} 3 & 3 & 5 \\-3 & -4 & -2 \end{bmatrix} \)
• C. \( \begin{bmatrix} 3 & 3 & -5 \\-3 & -4 & -2 \end{bmatrix} \)
• D. \( \begin{bmatrix} -3 & -3 & -5 \\ 3 & 4 & 2 \end{bmatrix} \)

Hint:

To avoid sign mistakes when solving algebra with matrices like \( A+B+C=O \), compute the sum element-by-element first, then flip the sign of every single component to reveal \( C \).

Answer 1

The Correct Option is C