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- E. On the right: a. r*ak + r*(-ak) = r*(ak + (-ak)) b. r*(ak + (-ak)) = r*0 c. r*0 = 0 F. So, r*(aj + (-ak)) = 0 G. Then, (aj + (-ak)) = 0 H. Then, (aj + (-ak)) + ak = 0 + ak II. On the left: (aj + (-ak)) + ak = aj + ((-ak) + ak) aj + ((-ak) + ak) = aj + 0 aj + 0 = aj On the right: 0 + ak = akThe rooms in a house are adjacent as indicated in the following table. An *' means they are adjacent, and a '-'means they are not. Rm LMNOPQRST L-- **** M---- N* 0 P Q R S T + * -- * * * ** - ✰✰✰ * |_ - --- * * - How few colors can be used so that each room is painted a color so in which no two adjacent rooms are the same color? List the rooms in groups with the same color, with the groups separated by semicolons (i.e. FE; A; GBD; C).please prove!