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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
The matrix $A = \frac{1}{3}\left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ - 2}\\{ - 2}&2&{ - 1}\end{array}} \right]$is
  • ✓
    Orthogonal
  • B
    Involutory
  • C
    Idempotent
  • D
    Nilpotent
✓

Answer

Correct option: A.
Orthogonal
a
(a) Since for given $A = \frac{1}{3}\left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ - 2}\\{ - 2}&2&{ - 1}\end{array}\,} \right]$
$A{A^T} = {A^T}A = {I_{(3 \times 3)}}$. Thus  $ A $ is orthogonal.

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