Question 1210438
<br>
{{{P=matrix(2,2,x^2,3,1,3x)}}}<br>
{{{Q=matrix(2,2,3,6,2,x)}}}<br>
The entry in row 2 column 1 of matrix PQ is {{{(1)(3)+(3x)(2)=3+6x}}}<br>
The entry in row 2 column 1 of matrix QP is {{{(2)(x^2)+(x)(1)=2x^2+x}}}<br>
those entries are the same, so<br>
{{{3+6x=2x^2+x}}}
{{{2x^2-5x-3=0}}}
{{{(2x+1)(x-3)=0}}}<br>
{{{x=-1/2}}} or {{{x=3}}}<br>
The positive solution is<br>
ANSWER: x=3<br>