I would like to know in particular whether a full rank matrix necessarilly has a determinant equal to/different from zero. Also, would the answer change based on the matrix being squared or not?
Matrices – Relation Between Full Rank Matrix and Its Determinant
determinantmatricesmatrix-rank
Best Answer
A full ranked matrix has a determinant different than zero. Squaring the matrix will still give us a full ranked matrix with determinant different than zero. This is due to the fact that a matrix has determinant other than zero iff it is invertible, and that is iff the matrix is full ranked.