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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
If $A$  is a square matrix $A + {A^T}$ is symmetric matrix, then $A - {A^T}$=
  • A
    Unit matrix
  • B
    Symmetric matrix
  • ✓
    Skew symmetric matrix
  • D
    Zero matrix
✓

Answer

Correct option: C.
Skew symmetric matrix
c
(c) ${(A - {A^T})^T} = {A^T} - {({A^T})^T}$

= ${A^T} - A$

= $ - (A - {A^T})$

So, $A - {A^T}$ is a skew symmetric matrix.

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