Can I Modify Order to Get X=I Matrix?

Thread starter somebody2
Start date Oct 23, 2008
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Identity Matrix

In summary, you can modify your order to get an identity matrix by changing the values in the original matrix to match the values in the identity matrix. This can be done using elementary row operations such as swapping rows, multiplying a row by a non-zero constant, or adding a multiple of one row to another. However, it is only possible to modify a square matrix to get an identity matrix, and the determinant of the original matrix will be changed to 1 after modification. If the original matrix is not invertible, it cannot be modified to an identity matrix.

Oct 23, 2008

somebody2

If I have ABCXC^-1A^-1B^-1=I (that is C, B, A inverse), can I modify the order so that the AA^-1, BB^-1 are multiplied to get the identity matrix so that I can get it down to X=I?

Last edited: Oct 23, 2008

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Oct 23, 2008

nizi

It's a clue to change the equation so that it keeps the equality.
For example trying premultiplying the inverse of A...

Last edited: Oct 23, 2008

1. Can I modify my order to get an identity matrix?

Yes, you can modify your order to get an identity matrix. This can be done by changing the values in the original matrix to match the values in the identity matrix.

2. How do I modify my order to get an identity matrix?

To modify your order to get an identity matrix, you can use elementary row operations such as swapping rows, multiplying a row by a non-zero constant, or adding a multiple of one row to another. These operations will change the values in the original matrix to match the values in the identity matrix.

3. Is it possible to modify any matrix to get an identity matrix?

No, it is not possible to modify any matrix to get an identity matrix. The original matrix must be a square matrix, meaning it has an equal number of rows and columns, in order for it to be modified to an identity matrix.

4. Will modifying my order to get an identity matrix change the determinant?

Yes, modifying your order to get an identity matrix will change the determinant. The determinant of the identity matrix is always equal to 1, so if you modify your order to get an identity matrix, the determinant of the original matrix will also become 1.

5. Can I modify an order to get an identity matrix if the original matrix is not invertible?

No, you cannot modify an order to get an identity matrix if the original matrix is not invertible. An invertible matrix is a square matrix with a non-zero determinant, which is necessary in order to modify the order and get an identity matrix. If the original matrix is not invertible, it does not have a unique solution and therefore cannot be modified to an identity matrix.