if the matrix a is both symmetric and skew-symmetric, show that a is a zero matrix.
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𝐏𝐫𝐨𝐯𝐞 𝐭𝐡𝐚𝐭 𝐀 𝐦𝐚𝐭𝐫𝐢𝐱 𝐰𝐡𝐢𝐜𝐡 𝐢𝐬 𝐛𝐨𝐭𝐡 𝐒𝐲𝐦𝐦𝐞𝐭𝐫𝐢𝐜 𝐚𝐬 𝐰𝐞𝐥𝐥 𝐚𝐬 𝐒𝐤𝐞𝐰 𝐬𝐲𝐦𝐦𝐞𝐭𝐫𝐢𝐜 𝐢𝐬 𝐚 𝐧𝐮𝐥𝐥 𝐦𝐚𝐭𝐫𝐢𝐱.