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Let omega ne 1 be a cube root of unity ...

Let ` omega ne 1` be a cube root of unity and S be the set of all
non-singular matrices of the form `[[1,a,b],[omega,1,c],[omega^(2),omega,1]]`, where
each of a, b, and c is either `omega or omega^(2)`. The number of
distinct matrices in the sat S is

A

2

B

6

C

4

D

8

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Consider the following statements: (i) If any two rows or coluns of a ...

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  2. Let A be a square matrix all of whose entries are integers. Which on...

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  3. Let omega ne 1 be a cube root of unity and S be the set of all non-...

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  4. Let M and N be two 3xx3 non-singular skew-=symmetric matrices such t...

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  5. The number of values of k which the linear equations 4x+ky+2z=0 kx...

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  6. The number of values of k, for which the system of equations (k""+""...

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  7. If P=[[1,alpha,3],[1,3,3],[2,4,4]] is the adjoint of a 3xx3 matrix A a...

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  8. If {:|(x,x),(1,x)| = |(3,4),(1,2)|. Write the positive value of 'x'.

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  9. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

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  10. If A is a square matrix order 3 such that |adjA|=225, find |A'|.

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  11. Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|= 2(a+b+c)^3

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  12. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  13. Using Cofactors of elements of third column, evaluate triangle - |[1,x...

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  14. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

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  15. Find the inverse of the matrix A = {:[(a,b),(c,(1+bc)/a)] and show tha...

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  16. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

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  17. If A = [[2,-3,5],[3,2,-4],[1,1,-2]] find A^-1. Using A^-1 solve the s...

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  18. Let P = [[3, -1, -2],[2 ,0 ,alpha ],[3, -5, 0]], where alpha in R. Sup...

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  19. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

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  20. Let M and n be two 3xx3 matrices such that MN = NM. Further, If Mne ...

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