Shear matrix/Product form/Exercise

Show that the shear matrix

${}A_{ij}(a)=E_{n}+aB_{ij}\,$

may be written as a matrix product ${}M\circ N\circ L$,where ${}M$ and ${}L$ are diagonal matrices

and ${}N$ is a shear matrix of the form ${}A_{ij}(1)$.

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