# Question:Can all 4x4 matrices be written as a product of the matrices S and R that i've defined?

## Question:Can all 4x4 matrices be written as a product of the matrices S and R that i've defined?

Hi! Any help would be greatly appreciated :)

I have two matrices S and R, where

S :=

Matrix([[a_1, a_2, a_3, a_4], [b_1, b_2, b_3, b_4], [c_1, c_2, c_3, c_4], [d_1, d_2, d_3, d_4]]);

such that

`a_1*d_1 = b_1*c_1a_2*d_2 = b_2*c_2a_3*d_3 = b_3*c_3a_4*d_4 = b_4*c_4;`
`and `
`R :=`
`Matrix([[s_1, t_1, r_1, l_1], [s_2, t_2, r_2, l_2], [s_3, t_3, r_3, l_3], [s_4, t_4, r_4, l_4]]);`
`such that `
`s_1*l_1 = t_1*r_1s_2*l_2 = t_2*r_2s_3*l_3 = t_3*r_3s_4*l_4 = t_4*r_4.`
`Now I have a specific matrix T, where`
`T := Matrix( [ [1, 0, 0, 1], [0, 1, 0, 0], [0, 1, 0, 0], [1, 0, 0, 1] ] );`
`I want to know if there is a solution to T = S*R. `
`Someone has already showed me that indeed`
`a solution to this exists (there are 90 solutions). `
`But now, this might be a stretch, but I'd like to know if, `
`in general, any 4x4 matrix can be written as a `
`product of matrices of the form S and R `
`(where S and R satisfy those constraints). `
`Thanks for your help!`
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