If P =[x+3x+2x+1x−1] = [ x + 3 x + 2 x + 1 x − 1 ] evaluate x if |P| = -10

If P $=\left[\begin{array}{cc}x+3& x+2\\ x+1& x-1\end{array}\right]$ evaluate x if |P| = -10

Answer Details

$P=\left[\begin{array}{cc}x+3& x+2\\ x+1& x-1\end{array}\right]$ evaluate x if |P| = -10
(x+3)(x-1) - {(x+1)(x+2)} = -10
x2 - x + 3x - 3 - {x2 + 2x + x + 2} = -10
x2 + 2x - 3 - {x2 + 3x + 2} = -10
-x - 5 = -10
-5 + 10 = x
5 = x
∴x = 5