Home
Class 12
MATHS
Let A and B be 2xx2 matrices with real e...

Let A and B be `2xx2` matrices with real entries . Let I be the `2xx2` indentity matrix. Denote by tr (A) the sum of diagonal entries of A .
Statement -1 : AB -BA `ne` I
Statement -2 : tr (A+B ) = tr (A) +tr (B) and tr (AB) =tr (BA)

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. AIEEE /JEE Main Papers|71 Videos
  • MATHEMATICAL REASONING

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B. ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos
  • PARABOLA

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTRE ENTRANCE EXAMINATION PAPERS|9 Videos

Similar Questions

Explore conceptually related problems

Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A^2=""I . Statement 1: If A!=I and A!=""-I , then det A""=-1 . Statement 2: If A!=I and A!=""-I , then t r(A)!=0 .

9, Let A be a 2 x 2 matrix with real entries. Let I be the 2 × 2 2identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2 -1 nvo bud o malai Statement 1: If A 1 and A?-1, then det A =-1. Statement 2: If A 1 and A?-I, then tr (A)?0 A. Statement 1 is false, statement 2 is true. B. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 . C. Statement 1 is true, statement 2 is true; statement 2 is nota correct explanation for statement 1. D. Statement 1 is true, statement 2 is false.

Let A be a 2xx2 matrix with non zero entries and let A^(2)=I , where I is 2xx2 identity matrix. Define Tr(A)= sum of diagonal elemets of A and |A|= determinant of matrix A. Statement 1: Tr(A)=0 Statement 2: |A|=1 .

Let A be a 2xx2 matrix with non-zero entries and let A^2=""I , where I is 2xx2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A. Statement-1: T r(A)""=""0 Statement-2: |A|""=""1 (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Let A = (a_(ij)_(3xx2) be a 3xx2 matrix with real entries and B = AA. Then

Let A be a 2xx2 matrix with non-zero entries and let A^(^^)2=I, where i is a 2xx2 identity matrix,Tr(A)i=sum of diagonal elements of A and |A|= determinant of matrix A.Statement 1:Tr(A)=0 Statement 2:|A|=1

Let A and B be two 2 xx 2 matrix with real entries, If AB=0 and such that tr(A)=tr(B)=0then

Let A be a square matrix of order 3 satisfying A A'=I Statement I A'A=I Statement II (AB)'= B'A'

Let A and B be any two 3xx3 matrices . If A is symmetric and B is skew -symmetric then the matrix AB-BA is :

MCGROW HILL PUBLICATION-MATRICES-Questions from Previous Years. B -Architecture Entrance Examination Papers
  1. If A and B are square matrics of the same order then which one of the ...

    Text Solution

    |

  2. Let A =[(1,1,0),(0,1,0),(0,0,1)] and let I denote the 3xx3 identity ma...

    Text Solution

    |

  3. Let A and B be 2xx2 matrices with real entries . Let I be the 2xx2 ind...

    Text Solution

    |

  4. Let A=[[a,b],[c,d]] be a 2xx2 real matrix. If A-alphaI is invertible f...

    Text Solution

    |

  5. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

    Text Solution

    |

  6. Let A=[(a,b),(c,d)]be a 2 xx 2 matrix, where a, b, c, d take value 0 t...

    Text Solution

    |

  7. Let S be the set of all real matrices A = [(a,b),(c,d)] such that a+d ...

    Text Solution

    |

  8. If S(n) denotes the sum of first n natural numbers.the [S(1)+S(2)x+S(3...

    Text Solution

    |

  9. Let A = [(1,1),(0,1)] and B = [(b(1),b(2)),(b(3),b(4))] . If 10 A^(10...

    Text Solution

    |

  10. If for a matrix A, absA=6and adj A={:[(1,-2,4),(4,1,1),(-1,k,0)]:}, th...

    Text Solution

    |

  11. Let S be the set of all real values of a for which the following syste...

    Text Solution

    |

  12. If A = ((2,52,152),(4,1-6,358),(6,162,620)) then the determinant of ad...

    Text Solution

    |

  13. Let S be the set of all real values of lambda for which the system of ...

    Text Solution

    |

  14. Ifthe equations a(y +z) =x,b(z+x) = y, c (x + y) = z have nontrivial...

    Text Solution

    |

  15. If B = [(-2,-2),(-1,0)] and A is a matrix such that A^(-1) B = B^(-1) ...

    Text Solution

    |

  16. Let [(3a,b,c),(b,3c,a),(c,a,3b)] be a 3xx3 matrix where a,b,c in R . I...

    Text Solution

    |

  17. The value of a for which the system linear of equations x+ay+z=1 a...

    Text Solution

    |

  18. Suppose A is a 2xx2 matrix for which A^(2)+A+I(2)=O(2) then det (adj (...

    Text Solution

    |

  19. If the system of linear equations : x+4y-3z=2 2x+7y+4z=alpha -x-...

    Text Solution

    |

  20. Let (a,b) be the solution of the system [(x,y)][(1,3),(5,1)]=[(2,1)]...

    Text Solution

    |