Discussion Forum

1)

If A = $\begin{bmatrix}0 & c & -b \\-c & 0 & a \\b & -a & 0 \end{bmatrix}$

and B =$\begin{bmatrix}a^{2} & ab & ac \\ab & b^{2} & bc \\ac & bc & c^{2} \end{bmatrix}$

then AB is equal to

Answer:

Option C

Explanation:

AB = $\begin{bmatrix}0 & c & -b \\-c & 0 & a \\b & -a & 0 \end{bmatrix}$$\begin{bmatrix}a^{2} & ab & ac \\ab & b^{2} & bc \\ac & bc & c^{2} \end{bmatrix}$

=$\begin{bmatrix}abc-abc & b^{2}c-b^{2}c & bc^{2}-bc^{2}\\-a^{2}c+a^{2}c & -abc+abc & -ac+ac \\a^{2}b-a^{2}b & ab^{2}-ab^{2} & abc-abc\end{bmatrix}$

=$\begin{bmatrix}0& 0 & 0 \\0 & 0 & 0 \\0 & 0 & 0 \end{bmatrix}$ = 0