zero matrix is in reduced row-echelon form

The homogeneous linear system has only two possibilities for its solutions

The homogeneous linear system can only have a trivial solution

The homogeneous linear system can have nontrivial solutions

The homogeneous linear system can have no solution

in scalar multiplication we multiply a row vector by a column vector

when we multiply a number to a matrix of linear system, we multiply it to either one row or one column

To multiply two matrices A and B, the number of columns of A must be the same number of rows of B

The resulting matrix for multiplying A and B has the same number of rows as A and the same number of columns as B

With matrices, multiplication is not commutative

Zero matrix can't come in all different shapes and sizes

Identity matrix can come in all different shapes and sizes

If AX = I (identity matrix), then A is called invertible

If AX = I (identity matrix), We can get the value of X if we do this operation (1/A)

which sentence is true

if A is a n x n matrix, then the reduced row echelon form of A is I (identity matrix)

if A is a n x n matrix, then the equation AX = b has exactly one solution for every n x 1 vector b

if A is a n x n matrix, then the equation AX = 0 has exactly one solution.

If A is invertible, then AX = b has exactly one solution, namely A^-1 b

If A is not invertible, then AX = b has no solution

If A is n x n invertible matrix, then KA is invertible for any nonzero scalar n; (KA)^-1 = (1/k)A^-1