First slide

Applications of determinant

Question

Let A be 3×3 matrix such that A is orthogonal and idempotent, then

Moderate

A

A must be symmetric
B

$\det (A) = - 1$
C

$A + A^{- 1} = 1$
D

none of these

Solution

$A A^{'} = I$ and $A^{2} = I$
$\begin{array}{l} ∴ A A^{'} = A^{2} \Rightarrow A^{- 1} (A A^{'}) = A^{- 1} A^{2} \\ \Rightarrow A^{'} = A \end{array}$

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