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If is a 2 xx 2 identity matrix, then | ...

If is a ` 2 xx 2` identity matrix, then `| (3I)^(30)|^(-1)` =_____.

A

`(1)/(3^(30))`

B

`(1)/(3^(60))`

C

`3^(30)`

D

`3^(60)`

Text Solution

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The correct Answer is:
B
If A is an ` n xx n` matrix, then `|kA| = k^(n)|A|` and det I = 1.
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PEARSON IIT JEE FOUNDATION-MATRICES-EXERCISE CONCEPT APPLICATION (LEVEL 1)
  1. If |A| = 47, then find |A^(T)|.

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  2. There are 25 software engineers and 10 testers in Infosys and 15 softw...

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  3. If det (A) = 5, then find det (15A) where A is of order 2 xx 2

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  4. If A = [{:("cosce"alpha, "tan"alpha), ("cot" alpha, "-sin"alpha):}], ...

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  5. Which of the following statements is true?

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  6. What is the condition that is to be satisfied for the identify (P +Q) ...

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  7. Solve the simultaneous equations: 2x-3y = 11 and 5x + 4y =16

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  8. If is a 2 xx 2 identity matrix, then | (3I)^(30)|^(-1) =.

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  9. If A is 2 xx 2 square matrix, such that det A = 9, then det (9A) =.

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  10. Which of the following statement (s) is true?

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  11. If A and B are two square matices such that AB= A and BA = B, then fin...

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  12. If A = [{:(3, 4), (-1, 2):}] " and B"= [{:(2, -3), (4, -5):}] , then f...

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  13. If the trace of the matrix A is 4 and the trace of matrix B is 7, the...

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  14. If the trace of the matrix A is 5, and the trace of the matrix B is 7,...

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  15. If A = [{:(3, 0), (0, 3):}], then find A^(n), (where n in N)

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  16. If A is a 2 xx 2 scalar matrix and 7 is the one of the elements in its...

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  17. A(1), A(2), A(3), ……, A(n) " and " B(1), B(2), B(3), …., B(n) are non-...

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  18. If A = [{:(5, 6), (9, 9):}], B= [{:(1, 3), (p, 3):}] and AB = BA, then...

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  19. The inverse of a scalar matrix A of order 2 xx 2, where one of the pri...

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  20. If A = [{:(3, -2),(6, 4):}], " then AA"^(-1) =.

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