116. Given that the determinant of the matrix
     
     is –12, the determinant of the matrix
     

1. 1. –96

   
   
   

   2. –24

   
   
   

   3. 24

   
   
   

   4. 96

   
   
   

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   Correct Option: A

   
   

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117. For which value of x will the matrix given below become singular?
     

1. 1. 4

   
   
   

   2. 6

   
   
   

   3. 8

   
   
   

   4. 12

   
   
   

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   Correct Option: A

   
   

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118. Consider the matrix:
     
     The number of distinct eigenvalues of P is:

1. 1. 3

   
   
   

   2. 0

   
   
   

   3. 1

   
   
   

   4. 2

   
   
   

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   Correct Option: C

   
   

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119. Consider the matrix P =
     
     Which one of the following statements about P is INCORRECT?

1. 1. Determinant of P is equal to 1.

   
   
   

   2. P is orthogonal.

   
   
   

   3. Inverse of P is equal to its transpose.

   
   
   

   4. All eigenvalues of P are real numbers.

   
   
   

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   The eigenvalues of an orthogonal matrix are of magnitude 1 and are real (s) complex conjugate pairs.
   

   Correct Option: D

   The eigenvalues of an orthogonal matrix are of magnitude 1 and are real (s) complex conjugate pairs.
   

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120. A real square matrix A is called skew– symmetric if

1. 1. A^T = A

   
   
   

   2. A^T = A^-1

   
   
   

   3. A^T = –A

   
   
   

   4. A^T = A + A^-1

   
   
   

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   A is skew-symmetric
   ∴ A^T = – A

   Correct Option: C

   A is skew-symmetric
   ∴ A^T = – A

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