Final answer:
If a matrix has linearly independent columns, the matrix has full column rank, and if it's square, it's invertible. Its columns also form a basis for its column space, which implies they are mutually perpendicular in three-dimensional space.
Step-by-step explanation:
If a matrix a has linearly independent columns, then it means that none of the columns in the matrix can be written as a linear combination of the others.
Consequently, one statement that must be true is that the matrix has full column rank; that is, the rank of the matrix is equal to the number of columns. This implies that the matrix is invertible if it is square, and its columns form a basis for the column space of the matrix.
Hence, option b is generally the one that must be true: 'All three are mutually perpendicular to each other' (considering it in a three-dimensional space and assuming the statement pertains to the vectors represented by the columns being orthogonal to each other).