https://file.aiquickdraw.com/mathbot/file/17282618281718kswl09w.jpg

The statement in the image is:

"If matrix \( A \) and matrix \( B \) are inverses of each other, then \( A \cdot B = I \), where \( I \) is the identity matrix."

This statement is **True**. 

If two matrices \( A \) and \( B \) are inverses of each other, by definition, their product \( A \cdot B \) (and equivalently \( B \cdot A \)) results in the identity matrix \( I \). Mathematically, this can be written as:

\[
A \cdot B = B \cdot A = I
\]

Where \( I \) is the identity matrix of the same size as \( A \) and \( B \). The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere, and it acts as the multiplicative identity in matrix operations (similar to how 1 is the identity for real numbers in multiplication).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the inverse of a 2x2 matrix?
2. What properties must a matrix satisfy to have an inverse?
3. Can all matrices have an inverse? Why or why not?
4. What is the determinant's role in determining if a matrix has an inverse?
5. How do matrix inverses relate to systems of linear equations?

**Tip:** The product of a matrix and its inverse always equals the identity matrix, but not all matrices have an inverse. For a matrix to have an inverse, it must be square and have a non-zero determinant.

If matrix A and matrix B are inverses of each other, then A · B = I, where I is the identity matrix.

Understand the relationship between matrix inverses and the identity matrix with this clear explanation. Learn how the product of inverse matrices always results in the identity matrix and key properties of invertible matrices. This is a core concept in linear algebra, suitable for college-level studies.

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