For a natural number n, let Cn = {(aij) € M,(R) : dij = Axı for all i, j,k,l such that j - i=nl- k}. - (a) Exactly one o

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For A Natural Number N Let Cn Aij M R Dij Axi For All I J K L Such That J I Nl K A Exactly One O 1 (116.02 KiB) Viewed 27 times

For a natural number n, let Cn = {(aij) € M,(R) : dij = Axı for all i, j,k,l such that j - i=nl- k}. - (a) Exactly one of the two matrices below is an element of C3. Which one? [1 mark] 1 *=6??) --6) 0 2 0 1 2 1 2 0 2 0 1 Aj A2 = 1 2 0 20 6) Let A be the matrix you chose in part (a). Compute A”. Check that A2 € C3, and write out a brief explanation (one or two sentences is enough) explaining how you checked. [2 marks] (c) Give a complete proof that C3 is a ring. You may assume that M3(R) is a ring. Hint: make as much use of that assumption as possible in your proof. [7 marks] MacBook Pro