I am completey lost on this. I know a matrix $B$ is congruent to $A$ if $B = P^\top\!\!AP$ but I tried finding the e-vectors and e-values for $P$ and $P^\top\!$ to spit out $A$ again. I really don't get how you are supposed to find $$ P = \operatorname{diag} \biggl( \frac{1}{\sqrt{3}}, 4, \frac12 \biggr). $$
Am I missing something?