Let 𝐴 be an invertible square matrix. It is possible for 𝐴 to have a column of zeros.

Question 1 Select one:
True
False

The statement is **False**.

### Explanation:
An invertible (or nonsingular) square matrix \( A \) has a **nonzero determinant** and **full rank** (i.e., all its columns are linearly independent). If \( A \) had a column of zeros, it would mean that at least one column is a linear combination of other columns (specifically, a zero vector). This would cause the determinant to be **zero**, making \( A \) **singular** (non-invertible). 

Since an invertible matrix **must** have full column rank, it **cannot** have a column of zeros.

### Answer:  
**False** ✅

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#### Related Questions:
1. If a square matrix has a row of zeros, can it be invertible?
2. What is the determinant of a matrix with a column of zeros?
3. How can you check if a matrix is invertible?
4. Can a non-square matrix be invertible?
5. What properties does an invertible matrix satisfy?

#### Tip:  
A square matrix \( A \) is invertible **if and only if** its determinant is nonzero and its rank is equal to its order (number of rows/columns).

Let 𝐴 be an invertible square matrix. It is possible for 𝐴 to have a column of zeros.

Learn why an invertible matrix cannot have a column of zeros. This problem involves concepts like matrix rank, determinant, and the conditions for matrix invertibility. The solution explains why a matrix with a zero column is singular and cannot be inverted. Suitable for students in Grades 11-12.

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