11. If \( \mathbf{A} \) is an \( m\times n \) matrix, then \( \mathbf{A}\mathbf{A}^{\mathrm{T}} \) and \( \mathbf{A}^{\mathrm{T}}\mathbf{A} \) have the same nullity.
11. If \( \mathbf{A} \) is an \( m\times n \) matrix, then \( \mathbf{A}\mathbf{A}^{\mathrm{T}} \) and \( \mathbf{A}^{\mathrm{T}}\mathbf{A} \) have the same nullity.