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AP EAMCET202018 Sep 2020Evening ShiftMathematicsMatricesActual

If (A ) is a Skew-symmetric matrix then (given (n N )) 1. (A^ 2 n ) is Skew-symmetric matrix. 2. (A^ 2 n+1 ) is Skew-symmetric matrix.

Options

  1. A1 is true, 2 is false
  2. BBoth 1 and 2 are true
  3. CBoth 1 and 2 are false
  4. D1 is false, 2 is true

Correct answer

D. 1 is false, 2 is true

Step-by-step solution

Given, (A ) is a skew symmetric matrix ( aligned A^T & =-A (A^ 2 n )^T= (A^T )^ 2 n =(-A)^ 2 n (A^ 2 n )^T & =A^ 2 n aligned ) ( A^ 2 n ) is Symmetric Matrix ( aligned & (A^ 2 n+1 )^T= (A^T )^ 2 n+1 =(-A)^ 2 n+1 & (A^ 2 n+1 )^T=-A^ 2 n+1 aligned ) (A^ 2 n+1 ) is skew symmetric Hence, option (d) is correct.

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