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If a square matrix A is involutory, the...

If a square matrix A is involutory, then `A^(2n+1)` is equal to

A

I

B

A

C

`A^(2) `

D

`(2n +1) A`

Text Solution

Verified by Experts

The correct Answer is:
B
`because A^(2n+1) = (A^(2))^(n) cdot A = (I)^(n) cdot A = IA = A`
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ARIHANT MATHS-MATRICES -Exercise (Single Option Correct Type Questions)
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  3. If a square matrix A is involutory, then A^(2n+1) is equal to

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  4. If [[cos theta,sin theta],[-sin theta,cos theta]], then lim (n rarr i...

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  10. Let A be a nxxn matrix such thatA ^(n) = alpha A, where alpha is a ...

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  12. The number of 2x2 matrices X satisfying the matrix equation X^2=I(Ii s...

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  13. if A and B are squares matrices such that A^(2006)=O and A B=A+B, then...

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  14. If P = [[cos frac(pi)(6), sin frac(pi)(6) ],[-sinfrac(pi)(6),cosfrac(p...

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  16. If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos ...

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  18. If Aa n dB are two non-singular matrices of the same order such that B...

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  20. If A is a square matrix of order 3 such that abs(A)=2, then abs((adj...

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