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3 and 4 .Determinants and Matrices
easy
The matrix $A = \frac{1}{3}\left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ - 2}\\{ - 2}&2&{ - 1}\end{array}} \right]$is
A
Orthogonal
B
Involutory
C
Idempotent
D
Nilpotent
Solution
(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.
Standard 12
Mathematics