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Let A be a 2xx2 matrix with real en...

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` .

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To solve the problem, we need to analyze the given statements about the 2x2 matrix \( A \) such that \( A^2 = I \), where \( I \) is the identity matrix. ### Step-by-Step Solution: 1. **Matrix Representation**: Let \( A \) be represented as: \[ A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} ...
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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 .

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

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Knowledge Check

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

    A
    `B^(-1)` is a `3xx3` matrix
    B
    `B^(-1)` is a `2xx2` matrix
    C
    `B^(-1)` does not exist
    D
    `B^(-1)` exists if and only if exactly one row of A consists of zeros

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

    A
    A and B are comutative w.r.t. operations of multiplication
    B
    A and B are not cummulative w.r.t operation of multiplication
    C
    A and B are both null matrices,0
    D
    BA=0

  • Let A be a square matrix of order 3 whose all entries are 1 and let I_(3) be the indentiy matrix of order 3. then the matrix A - 3I_(3) is

    A
    invertible
    B
    orthogonal
    C
    non-invertible
    D
    real skew symmetric matrix