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 correct answer is **False**.

If \( A \) is an invertible square matrix, it cannot have a column (or row) of zeros. This is because if any column (or row) is a zero vector, the determinant of the matrix would be zero, and a matrix with a zero determinant is not invertible.

Therefore, an invertible matrix must have full rank, meaning no columns or rows can be linearly dependent (including having a column of zeros).

Would you like further explanation or have more questions on this topic? 

Here are 5 related questions for you:
1. What is the condition for a matrix to be invertible?
2. How do you calculate the determinant of a matrix?
3. What does it mean for a matrix to be of full rank?
4. How does a column of zeros affect the rank of a matrix?
5. Can a matrix with a row of zeros be invertible?

**Tip**: To check if a matrix is invertible, always calculate its determinant—if it's non-zero, the matrix is invertible!

Let 𝐴 be an invertible square matrix. It is possible for 𝐴 to have a column of zeros. Select one: True False

Explore the properties of invertible matrices and why a matrix cannot have a column of zeros. This problem explains the key concepts of matrix inversion, determinants, and the full rank condition, suitable for high school students (Grades 11-12).

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