without actual expansion of this determinant prove that :
| 0 99 -998 |
|-99 0 997| = 0
|998 -997 0 |

Question

without actual expansion of this determinant prove that :    
            |  0       99      -998 |
            |-99       0         997|      = 0
            |998     -997       0  |

anonymous · Answer

$$\left[\begin{matrix}0 & 99 & -998 \ -99 & 0 & 997\ 998 & -997 & 0 \end{matrix}\right]$$

ganeshie8 · Answer

hint : skew symmetric matrix wid odd size

anonymous · Answer

I'm sorry. :( 
I feel so stupid right now :( 

I get that it's a skew symmetric matrix .. but idk how to proceed :(

ganeshie8 · Answer

for a skew symmetric matrix of size 3,    $det(A) = det(-A) = (-1)^3 det(A) = -det(A)$ 

$\implies    det(A) = 0$

ganeshie8 · Answer

see if u can digest above.
basically u need to see that u can get determinant by expanding any line : a row or a column

thus, for a skew symmetric matrix, det(A) equals det(-A)