https://file.aiquickdraw.com/mathbot/file/1726028205577lw2an5wi.jpg

Let's analyze each statement provided in the image and determine whether they are true or false:

1. **If a matrix is invertible, then its inverse is unique.**
   - **True.** If a matrix \(A\) is invertible, there exists a unique matrix \(A^{-1}\) such that \(A \times A^{-1} = I\), where \(I\) is the identity matrix. Uniqueness is guaranteed by the properties of matrix multiplication.

2. **If \(A\) and \(B\) are invertible, then \((AB)^{-1} = A^{-1}B^{-1}\).**
   - **False.** The correct formula is \((AB)^{-1} = B^{-1}A^{-1}\). The order of multiplication is reversed when taking the inverse of a product of two matrices.

3. **All square matrices are invertible.**
   - **False.** Not all square matrices are invertible. A square matrix is invertible only if its determinant is non-zero. A square matrix with a determinant of zero is called "singular" and does not have an inverse.

4. **Every identity matrix is invertible.**
   - **True.** The identity matrix \(I\) of any size is always invertible, and its inverse is itself, i.e., \(I^{-1} = I\).

### Conclusion:
The statements that are true are:
- **Statement 1:** If a matrix is invertible, then its inverse is unique.
- **Statement 4:** Every identity matrix is invertible.

Would you like more details or have any questions?

### Related Questions:
1. What is the definition of an invertible matrix?
2. How do you find the inverse of a 2x2 matrix?
3. What are some examples of non-invertible matrices?
4. Can a rectangular matrix be invertible?
5. How does the determinant relate to matrix invertibility?

### Tip:
Remember, for two matrices \(A\) and \(B\), \((AB)^{-1} = B^{-1}A^{-1}\). The order is reversed when taking the inverse of a product.

Select all of the following statements which are true:
1. If a matrix is invertible, then its inverse is unique.
2. If A and B are invertible, then (AB)^-1 = A^-1 B^-1.
3. All square matrices are invertible.
4. Every identity matrix is invertible.

Analyze a set of statements about matrix invertibility, including unique inverses, properties of square and identity matrices, and the inverse of matrix products. Understand key formulas such as (AB)^-1 = B^-1 A^-1 and the conditions for matrix invertibility.

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