# Math Help - matrix

1. ## matrix

Nice to see the forum back again. It has been down for weeks hasn't it?

A question says: "Cayley proved in 1946 that, if S is a skew-symmetric matrix, then I+S is non-singular and A=(I-S)(I+S)^-1 is orthogonal. Find A when S=(0 3, -3 0) and show that it is orthogonal."

The second row of S is -3 0. I don't know why I am not able to find A. I will probably manage the final part myself.

2. ## Re: matrix

$\begin{bamtrix}1 & 0\\ 0 & 1 \end{batrix}- \begin{bmatrix} 0 & 3\\ -3 & 0 \end{bmatrix} = \begin{bmatrix} 1 & -3 3 & 1 \end{bmatrix}$

So then what is I + S?

Let B=I+S. Then the inverse of B is
$\frac{1}{\text{det}(B)}\begin{matrix} b_{22} & -b_{21}\\ -b_{12} & b_{11} \end{bmatrix}$

3. ## Re: matrix

Is The Matrix,
| 0 3 |
| -3 0 |
And,
| 1 -3|
| 3 1 |

IF these are the two matrices please tell everyone, Please also Define I & S
A series of good videa tutorials on matrices can be found !

Sorry, didnt realise there was a post above the one shown on my screen. I see the question now i am just gonna leave my post as it is for now though. sorry.

4. ## Re: matrix

The first matrix you give is S. I had been making a mistake by multiplying by the determinant instead of dividing. The expression is straightforward to evaluate. The last part is done using the property AxAtranspose=I.