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QUESTION
What are some examples of matrices satisfying the following conditions, and can I prove that they do satisfy the conditions.
What are some examples of matrices satisfying the following conditions, and can I prove that they do satisfy the conditions.
(a) A 4 × 4 matrix A which has no zero row or column, is not upper or lower triangular, has at least 6 non-zero entries, and satisfies A−1 = AT .
(b) A 3 × 3 matrix A satisfying AT = A.
(c) Two non-equal 2 × 2 matrices A (diagonal) and B (non-diagonal, not the zero matrix) such that AB = BA.
