$(A^TA+aI)^{-1}A^T = A^TX$
where A and X are real-matrices and a is a positive non-zero real number. A is non-zero and you may assume that A is such that there is a unique X that satisfies the above equation.
$(A^TA+aI)^{-1}A^T = A^TX$
where A and X are real-matrices and a is a positive non-zero real number. A is non-zero and you may assume that A is such that there is a unique X that satisfies the above equation.
Using the inverse of the inverse so to speak:
$A^T=(A^TA+aI)A^TX$ $A^T=A^T(AA^T+aI)X$
and now if $X=(AA^T+aI)^{-1}$ it is solved.