Matrix Mania

Algebra Level pending

Consider a matrix $\text{A}^{m \times n}$ such that $\text{Rank(A)} = n < m$ . Then which of the following is true?

P.S. : $\text{A}^\prime$ denotes the transpose of the matrix $\text{A}$ and $\vert \text{A} \vert$ denotes the determinant of the matrix $\text{A}$ .

\vert \text{A}^\prime \text{A} \vert <0

\vert \text{AA}^\prime \vert \neq 0

\vert \text{AA}^\prime \vert =0

\vert \text{A}^\prime \text{A} \vert =0

1 solution

Samrit Pramanik
May 26, 2018

$\text{Rank(A)}= \text{Rank(AA}^\prime) = n <m$ . But $\text{AA}^\prime$ is a matrix of order $m \times m$ . So, $\vert \text{AA}^\prime \vert = 0$

Matrix Mania

1 solution

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