<prompt> Acha mathbfP iwe ndiyo matrix ya kuonyesha kwenye vekta beginpmatrix -3 -2 endpmatrix. Find mathbfP-1.Ikiwa inverse haipo, basi ingiza matrix ya sifuri.  <response>: Matrix ya makadirio daima ni ya fomuanzapmatrix cos2 theta cos theta sin theta cos theta sin theta sin2 theta mwishopmatrix,ambapo vekta inayokadiriwa kwenye ina mwelekeo wa vekta beginpmatrix cos theta sin theta endpmatrix. Kiamuzi cha matrix hii ni basicos2 theta sin2 theta - cos theta sin theta2 0,kwa hivyo kinyume hakipo, na jibu ni matrix sifuri anza pmatrix 0 0 0 0 mwishopmatrix. 