In general, how many key of [a] for 2-by-2 Hill cipher exist? Show your work. Please...

 

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In general, how many key of [a] for 2-by-2 Hill cipher exist? Show your work. Please follow these steps as guide to find the answer: If the determinant of the matrix, ad-bc is 13 or is even the matrix is not allowed. Therefore: a. Find the number of matrices whose determinant is even because one or both rows are even, i.e. all element of that row are even. b. Find the number of matrices whose determinant is even because one or both columns are even. c. Find the number of matrices whose determinant is even because all of the elements are odd. d. Considering overlaps, find the total number of matrices whose determinant is even. e. Find the number of matrices whose determinant is multiple of 13 because the first column is a multiple of 13. f. Find the number of matrices whose determinant is a multiple of 13 where the first column is not a multiple of 13 but the second column is a multiple of the first modulo 13. g. Find the total number of matrices whose determinant is a multiple of 13. h. Find the total number of matrices whose determinant is a multiple of 26 because they fit cases parts (a) and (e). (b) and (e). (c) and (e), (a) and (f), and so on. i. Find the total number of matrices whose determinant is neither a multiple of 2 nor a multiple of 13. In general, how many key of [a] for 2-by-2 Hill cipher exist? Show your work. Please follow these steps as guide to find the answer: If the determinant of the matrix, ad-bc is 13 or is even the matrix is not allowed. Therefore: a. Find the number of matrices whose determinant is even because one or both rows are even, i.e. all element of that row are even. b. Find the number of matrices whose determinant is even because one or both columns are even. c. Find the number of matrices whose determinant is even because all of the elements are odd. d. Considering overlaps, find the total number of matrices whose determinant is even. e. Find the number of matrices whose determinant is multiple of 13 because the first column is a multiple of 13. f. Find the number of matrices whose determinant is a multiple of 13 where the first column is not a multiple of 13 but the second column is a multiple of the first modulo 13. g. Find the total number of matrices whose determinant is a multiple of 13. h. Find the total number of matrices whose determinant is a multiple of 26 because they fit cases parts (a) and (e). (b) and (e). (c) and (e), (a) and (f), and so on. i. Find the total number of matrices whose determinant is neither a multiple of 2 nor a multiple of 13.