Question

If A = $\begin{bmatrix} 0 & - 1 & 2 \ 1 & 0 & 3 \

• 2 & - 3 & 0 \end{bmatrix}$, then A + 2A^T equals –

• A. A
• B. –A^T
• C. A^T
• D. 2A²

Answer 1

Answer: (C)

A^T

Answer 2

A^T = $\begin{bmatrix} 0 & 1 & - 2 \

• 1 & 0 & - 3 \ 2 & 3 & 0 \end{bmatrix}$, 2A^T =$\begin{bmatrix} 0 & 2 & - 4 \
• 2 & 0 & - 6 \ 4 & 6 & 0 \end{bmatrix}$2 A^T + A

= $\begin{bmatrix} 0 & 1 & - 2 \

• 1 & 0 & - 3 \ 2 & 3 & 0 \end{bmatrix}$ = A^T

Alternate

A^T = – A (Q A is skew symmetric)

So 2A^T + A = A^T + A – A = A^T.