Question

Select all statements below which are true for all invertible nxn matrices a and b?

1) The product of two invertible matrices is invertible
2) The inverse of a product of two matrices is the product of their inverses in reverse order
3) The transpose of an invertible matrix is invertible
4) The determinant of an invertible matrix is non-zero

Answer 1

All stated properties are true for invertible nxn matrices: the product of two invertible matrices is invertible, the inverse of a product is the product of the inverses in reverse order, the transpose of an invertible matrix is also invertible, and the determinant of an invertible matrix is always non-zero.

Step-by-step explanation:

True Statements for Invertible Matrices

For all invertible nxn matrices a and b:

1. The product of two invertible matrices is invertible.
2. The inverse of a product of two matrices is the product of their inverses in reverse order.
3. The transpose of an invertible matrix is invertible.
4. The determinant of an invertible matrix is non-zero.

Each of these statements is true and reflects fundamental properties of matrix algebra in the context of invertible matrices.