5. Italy and France combined for a total of 46 penalties during the 2006 FIFA World Cup. The penalties were a combination of fouls, yellow cards (cautions), and red cards (expulsions). There was one less red card than half the number of yellow cards and one more foul than 8 times the total number of cards. How many of each type of penalty were there during the match? 6. Michelle Tanner has a piggy bank that has 75 total coins in it that consists of nickels, dimes, and quarters. The total value of the money in the piggy bank is $12.75. The number of dimes is also twice the number of nickels in the piggy bank. How many of each coin (nickel, dime, quarter) does she have in the bank? Is it possible? a. Is it possible that two matrices, A and B, can be added but not multiplied? If so, give an example. If not, explain why. b. Is it possible that two matrices, A and B can be multiplied but not added? If so, give an example. If not, explain why. c. Is it possible for two matrices, A and B, to exist such that AB = BA ? If so, give an example. If not, explain why.