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Matrices and Determinants

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  1. 251.Let A=pmatrix1&-12&pmatrix and B=pmatrix&11&0pmatrix, ,R.
  2. 252.Let A and B be any two 33 symmetric and skew-symmetric matrices respectively.
  3. 253.Let A and B be two 33 non-zero real matrices such that AB is the zero matrix.
  4. 254.The number of matrices of order 33, whose entries are either 0 or 1 and the sum of all the…
  5. 255.Which of the following matrices can NOT be obtained from the matrix pmatrix-1&21&-1pmatrix…
  6. 256.Let X=pmatrix111pmatrix and A=pmatrix-1&2&30&1&60&0&-1pmatrix.
  7. 257.Let M be any 33 matrix with entries from the set 0,1,2.
  8. 258.If A=pmatrix0&-22&0pmatrix and (I_2+A)(I_2-A)^-1=pmatrixa&-b&apmatrix, then 13(a^2+b^2) is…
  9. 259.If for the matrix A=pmatrix1&-&pmatrix, AA^T=I_2, then the value of ^4+^4 is
  10. 260.Let A be a symmetric matrix of order 2 with integer entries.
  11. 261.If the matrix A=pmatrix1&0&00&2&03&0&-1pmatrix satisfies A^20+ A^19+ A=pmatrix1&0&00&4&00&…
  12. 262.Let A+2B=pmatrix1&2&06&-3&3-5&3&1pmatrix and 2A-B=pmatrix2&-1&52&-1&60&1&2pmatrix.
  13. 263.Let I be an identity matrix of order 22 and P=pmatrix2&-15&-3pmatrix.
  14. 264.Let A=pmatrixi&-i-i&ipmatrix, i=-1.
  15. 265.The total number of 33 matrices A having entries from the set 0,1,2,3, such that the sum o…
  16. 266.Let A=pmatrixa_1_2pmatrix and B=pmatrixb_1_2pmatrix be two 21 matrices with real entries s…
  17. 267.Let P=pmatrix-30&20&5690&140&112120&60&14pmatrix and A=pmatrix2&7&^2-1&-&10&-&-+1pmatrix, …
  18. 268.If A=pmatrix2&30&-1pmatrix, then the value of (A^4)+[A^10-Adj(2A)^10] is equal to .....
  19. 269.If A=pmatrix1&1&10&1&10&0&1pmatrix and M=A+A^2+A^3++A^20, then the sum of all the elements…
  20. 270.Let S=nN:pmatrix0&i1&0pmatrix^npmatrixa&b&dpmatrix=pmatrixa&b&dpmatrix , a,b,c,dR, where i…
  21. 271.If P=pmatrix1&01/2&1pmatrix, then P^50 is
  22. 272.Let A=[a_ij] be a real matrix of order 33, such that a_i1+a_i2+a_i3=1 for i=1,2,3.
  23. 273.Let A=pmatrix0&1&01&0&00&0&1pmatrix.
  24. 274.Let A=pmatrix1&-1&00&1&-10&0&1pmatrix and B=7A^20-20A^7+2I, where I is the identity matrix…
  25. 275.If A=pmatrix1√5&2√5-2√5&1√5pmatrix, B=pmatrix1&0&1pmatrix, i=-1, and Q=A^TBA, then the inv…
  26. 276.Let A be a 33 real matrix.
  27. 277.Let A=pmatrix1&2-1&4pmatrix.
  28. 278.Let A and B be two 33 real matrices such that (A^2-B^2) is an invertible matrix.
  29. 279.Let A=[a_ij] be a 33 matrix, where a_ij=cases(-1)^j-1&if i<j2&if i=j(-1)^i+j&if i>jcases.
  30. 280.If the matrix A=pmatrix0&2&-1pmatrix satisfies A(A^3+3I)=2I, then the value of K is
  31. 281.Let A=pmatrix1&0&00&1&11&0&0pmatrix.
  32. 282.Let be a root of x^2+x+1=0, and the matrix A=1√3pmatrix1&1&11&&^21&^2&^4pmatrix.
  33. 283.The number of all 33 matrices A, with entries from the set -1,0,1, such that the sum of th…
  34. 284.If A=pmatrix2&29&4pmatrix and I=pmatrix1&00&1pmatrix, then 10A^-1 is equal to:
  35. 285.If A=pmatrix&i&pmatrix, =24, and A^5=pmatrixa&b&dpmatrix, where i=-1, then which one of th…
  36. 286.Let A=pmatrixx&11&0pmatrix, xR, and A^4=[a_ij].
  37. 287.Let a,b,cR be all non-zero and satisfy a^3+b^3+c^3=2.
  38. 288.Let A=pmatrix0&2q&r&q&-r&-q&rpmatrix.
  39. 289.Let P=pmatrix1&0&03&1&09&3&1pmatrix and Q=[q_ij] be a 33 matrix such that Q-P^5=I_3.
  40. 290.Let A=pmatrix&-&pmatrix, R, such that A^32=pmatrix0&-11&0pmatrix.
  41. 291.The total number of matrices A=pmatrix0&2y&12x&y&-12x&-y&1pmatrix (x,yR, x y) for which A^…
  42. 292.If A is a symmetric matrix and B is a skew-symmetric matrix such that A+B=pmatrix2&35&-1pm…
  43. 293.Let A=pmatrix1&0&01&1&01&1&1pmatrix and B=A^20.
  44. 294.For two 33 matrices A and B, let A+B=2B^T and 3A+2B=I_3, where B^T is the transpose of B a…
  45. 295.If P=pmatrix√32&12-12&√32pmatrix, A=pmatrix1&10&1pmatrix, and Q=PAP^T, then P^TQ^2015P is:
  46. 296.If A=pmatrix0&-11&0pmatrix, then which one of the following statements is NOT correct?
  47. 297.If A=pmatrix1&2&22&1&-2&2&bpmatrix is a matrix satisfying the equation AA^T=9I, where I is…
  48. 298.If A=pmatrix1&2&x3&-1&2pmatrix and B=pmatrixy1pmatrix be such that AB=pmatrix68pmatrix, th…
  49. 299.Let A and B be any two 33 matrices.
  50. 300.If p,q,r are 3 real numbers satisfying the matrix equation pmatrixp&q&rpmatrixpmatrix3&4&1…