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If A a non singular matrix anA^T denotes...

If A a non singular matrix an`A^T` denotes the transpose of A then (A) `|A A^T|!=|A^2|` (B) `|A^T A|!=|A^T|^2` (C) `|A|+|A^T|!=0` (D) `|A|!=|A^T|`

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Knowledge Check

  • If a non-singular matrix and A^(T) denotes the tranpose of A, then

    A
    `|A|ne |A^(T)|`
    B
    `|A.A^(T)|=|A\|^(2)`
    C
    `|A^(T).A|=|A^(T)|^(2)`
    D
    `|A|=|A|^(T)ne0`

  • If "AA"^T=I where A^T is transpose of matrix A then, 1/2A[(A+A^T)^2+(A-A^T)^2]=?

    A
    `A^2`
    B
    `A^3+1`
    C
    `A^2+1`
    D
    `A^3+A^T`

  • If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A^T," then " B B^T equals

    A
    `B^(-1)`
    B
    `(B^(-1))^T`
    C
    `I+B`
    D
    `{:[(2015,0),(1,2015)]:}`

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