At t = 21:00, Strang covers the definition of inversion (and at 32:00 he gives an example): first suppose A is an n x m matrix. Then if you have a left inverse L that acts on A, it will produce an identity matrix, call it I_n; similarly, If you have a right inverse R, when A acts on R it will also produce an identity matrix, call it I_m. So a Matrix is non-singular (sometimes mistakenly called regular) only if  m = n, A is square, and det(A) (does not) = 0. In particular, if the matrix A have full rank = n, all its columns and rows would be independent, so A would be invertible.####[]