Multiple Choice Questions on A is m times n full rank matrix with m gt n and 39 I 39 is an identity matrix Let matrix A........... for NDA Exam Preparation

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Multiple Choice Questions

A is m times n full rank matrix with m gt n and 39 I 39 is an identity matrix Let matrix A...........

Mathematics (NDA) Matrices and Determinants
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    A is m × n, full-rank matrix with m>n, and 'I' is an identity matrix. Let matrix A’ =(ATA)-1AT then which one of the following is false?

    AA’A=A

    Incorrect Answer

    (A’A)2  =I

    Incorrect Answer

    A’A  =I

    Incorrect Answer

    AA’A=  -A

    Correct Answer
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    Explanation:

    Option a

    AA’A  =A[(ATA)-1 AT]A

    =A[(ATA)-1 ATA]

    =A[  P-1P]

    =A

    Option c

    A’A    = [(ATA)-1 ATA]

    =P-1 P

    =I

    Option a c, b is correct

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