Prove that this matrix is positive defined

Prove that this matrix is positive defined:

$<br />
A=<br />
\begin{pmatrix}</p>
<p>\:1                  &-\frac{1}{2}& -\frac{1}{2}&                   \:1 &-\frac{1}{2} &-\frac{1}{2} \\<br />
-\frac{1}{2} &                \:1  &-\frac{1}{2} &-\frac{1}{2}  &                 \:1 &-\frac{1}{2} \\<br />
-\frac{1}{2} &-\frac{1}{2} &                  \:1 &-\frac{1}{2} &-\frac{1}{2} &                 \:1   \\<br />
                  \:1  &-\frac{1}{2} &-\frac{1}{2}&                  \:1   &-\frac{1}{2}& -\frac{1}{2} \\<br />
-\frac{1}{2}  &                  \:1 &-\frac{1}{2} &-\frac{1}{2}  &                  \:1 &  -\frac{1}{2} \\<br />
-\frac{1}{2}  &-\frac{1}{2} &                  \:1  &-\frac{1}{2} &-\frac{1}{2} &                   \:1<br />
\end{pmatrix}<br />
 $

A matrix A is positive defined if:
$ <Ax,x>\geq0, \forall x=(x_1, x_2, x_3, x_4, x_5, x_6)^{T} $

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