using the properties of determinants, solve for x: |a+x a-x a-x a-x a+x a-x a-x a-x a+x| = 0

Let = a+xa-xa-xa-xa+xa-xa-xa-xa+xNow performing R1R1+R2+R3=3a-x3a-x3a-xa-xa+xa-xa-xa-xa+x=3a-x111a-xa+xa-xa-xa-xa+xNow performing C1C1-C2 and C2C2-C3, =3a-x001-2x2xa-x0-2xa+xNow applying R2R2+R3, =3a-x001-2x02a0-2xa+xnow expanding along R1 , =3a-x0-0+10-0=0

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