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How many 3xx3 matrices M with entries fr...

How many `3xx3` matrices `M` with entries from `{0,1,2}` are there, for which the sum of the diagonal entries of `M^T M` is 5? (A) 126 (B)198 (C) 162 (D) 135

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Knowledge Check

  • How many matrices X with entries {0,1,2} are there for which sum of diagonal entries of X.X^(T) is 7?

    A
    560
    B
    562
    C
    504
    D
    540

  • Let A, B be two 3xx3 matrices with entries from real number . Which one of the follwing is true ?

    A
    `(A+B)^(3)=A^(3) +3A^(2) B+3AB^(2)+B^(3)`
    B
    `(AB)^(2)=O implies AB=O `
    C
    `(A+B)(A-B)=A^(2)-B^(2)`
    D
    `(A+B) A=BA+A^(2)`

  • If A=[(0,1,2),(1,2,3),(3,1,1)] , then the sum of the all the diagonal entries of A^(-1) is

    A
    2
    B
    3
    C
    `-3`
    D
    4

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