Let A be n xn matrix that has zeros on the main diagonal and ones everywhere else. Example of a 4 x 4 matrix of this type is given below 1 1 1 1 11 1 1 1 1 (3a ) Compute det(A) and A-l for n = 2, 3,4. (3b, s) Note that in the cases n = 2, 3, 4 the matrix A- has a special structure (all the elements on the diagonal are the same and all the off-diagonal elements are also the same). Guess a formula for A in the general case (or arbitrary n) and verify that your guess is correct by checking that AA = I.

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