# If A is a matrix such that a 11= a 12 =a 13=1, a 21= 0 , a 22= 1, a 23= 1 ,a 31=0, a 32= 0 , a 33= 1 , then use the principle of mathematical induction to show that An is equal to a 11 = 1, a 12= n , a 13 = n(n+1)/2 , a 21 = 0 , a 22=1, a 23=n, a 31=0, a 32=0 , a 33=1 for every positive integers n .

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