Question

If \[ A = \begin{bmatrix} 0 & c & -b \\ -c & 0 & a \\ b & -a & 0 \end{bmatrix}, \quad B = \begin{bmatrix} a^2 & ab & ac \\ ab & b^2 & bc \\ ac & bc & c^2 \end{bmatrix}, \] then \( AB \) is equal to:

• A. \( B \)
• B. \( A \)
• C. \( O \)
• D. \( I \)

Hint:

Matrix multiplication can result in the zero matrix when matrices are orthogonal or in certain symmetric forms.

Answer 1

The Correct Option is C

When multiplying matrices \( A \) and \( B \), the result is the zero matrix \( O \), indicating that the matrices are orthogonal.
Final Answer: \[ \boxed{O} \]