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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
If  $A$  is a square matrix for which ${a_{ij}} = {i^2} - {j^2}$, then $A$ is
  • A
    Zero matrix
  • B
    Unit matrix
  • C
    Symmetric matrix
  • ✓
    Skew symmetric matrix
✓

Answer

Correct option: D.
Skew symmetric matrix
d
(d) ${a_{ji}} = {i^2} - {j^2}$ is a square matrix.

For a skew symmetric matrix ${a_{ji}} = -{a_{ji}}$

$\Rightarrow$ ${a_{ij}} = {i^2} - {j^2}$ and ${a_{ji}} = {j^2} - {i^2}$

$\Rightarrow$ ${a_{ij}} + {a_{ji}} = 0$

$\Rightarrow \,{a_{ij}} =  - {a_{ji}}$

Hence, $ {a_{ji}}$ is a skew symmetric matrix.

 

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