P is an orthogonal matrix and A is a periodic matrix with period 4 and Q = PAP^T then X = P^TQ^{2005

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3 and 4 .Determinants and Matrices

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$P$ is an orthogonal matrix and $A$ is a periodic matrix with period $4$ and $Q = PAP^T$ then $X = P^TQ^{2005}P$ will be equal to

A

$A$

B

$A^2$

C

$A^3$

D

$A^4$

Solution

$X = P^T[(PAP^T)(PAP^T)………(PAP^T)$ $P = A^{2005} = A^{2004}$ .$A = A$ Ans. Note :If $k$ is the period of $A ⇒ A^{nk+1} = A$ for $n \in I$

Standard 12

Mathematics

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