Defining a matrix, $\mathbf{X}$

$\mathbf{X}=(\mathbf{A}+\mu \mathbf{I})^{-1}\mathbf{B}$

where $\mathbf{B}$ is a $N\times M$ matrix, $\mathbf{A}$ is a $N\times N$matrix, $\mu$ is a scalar, and $\mathbf{I}$ is a $N\times N$ identity matrix.

We would like to find $\mu$, satisfying the following equation:

$tr(\mathbf{XX}^H)=c$

where $tr(.)$ shows trace operator, $c$ is a constant, and $\mathbf{X}^H$ is the Hermitian (complex transpose) of $\mathbf{X}$.

Thanks.