The maximum number of linearly independent vectors in a

**matrix**is equal to the number of non-zero rows in its row echelon**matrix**. Therefore, to find the**rank of a matrix**, we simply transform the**matrix**to its row echelon form and count the number of non-zero rows.Similarly, you may ask, when a matrix is invertible?

If this is the case, then the

**matrix**B is uniquely determined by A and is called the inverse of A, denoted by A^{−}^{1}. A square**matrix**that is not**invertible**is called singular or degenerate. A square**matrix**is singular if and only if its determinant is 0.How do you know if the inverse of a matrix exists?

**If**the determinant of the

**matrix**is zero, then it will not have an

**inverse**; the

**matrix**is then said to be singular. Only non-singular

**matrices**have inverses. Find the

**inverse**of the

**matrix**A = ( 3 1 4 2 ). result should be the identity

**matrix**I = ( 1 0 0 1 ).

Is an all zero matrix invertible?

square

**matrix**is not**invertible**if at least one row or column is**zero**.