Misc 14 - If matrix A is both symmetric and skew symmetric - Symmetric and skew symmetric matrices

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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Misc. 14 (Introduction) If the matrix A is both symmetric and skew symmetric, then A. A is a diagonal matrix B. A is a zero matrix C. A is a square matrix D. None of these Diagonal Matrix: Matrix with all non-diagonal elements zero. Eg: [■8(1&0&0@0&−2&0@0&0&4)] , [■8(−9&0@0&35)] Zero Matrix: Matrix with all elements zero Eg: [■8(0&0&0@0&0&0@0&0&0)] , [■8(0&0@0&0)] Square matrix Matrix with number of rows = Number of columns Eg: [■8(6&−2&2@−2&3&−1@2&−1&3)] , [■8(1&6@5&7)] Misc. 14 If the matrix A is both symmetric and skew symmetric, then A. A is a diagonal matrix B. A is a zero matrix C. A is a square matrix D. None of these Since A is both symmetric and skew-symmetric matrix, A’ = A and A’ = –A Comparing both equations ⇒ A = − A ⇒ A + A = O ⇒ 2A = O ⇒ A = O Therefore, A is a zero matrix.

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