Question

Prove or give a counterexample: if f: X rightarrow Y and g: Y rightarrow X are functions such that g o f = I_X and f o g = I_Y, then f and g are both one-to-one and onto and g = f^-1.
Help please! Using matlab

Answer 1

% index vectors for rows and columns
p = 1:m;
q = 1:n;
% index matrices for rows and columns
[P, Q] = ndgrid(p, q);
% create a matrix with the shift values
K = repmat(k(:), [1 n]);
% update the matrix with the column indexes
Q = 1 + mod(Q+K, n);
% create matrix of linear indexes
ind = sub2ind([m n], P, Q);
% finally, create the output matrix
B = A(ind);