Final answer:
The request lacks a complete matrix for inversion. For a 2x2 matrix, the inverse is found using a specific formula if the determinant is not zero. The question is most likely about matrix inversion in the context of mathematics.
Step-by-step explanation:
The question appears to be asking for the inverse of a matrix using an inversion algorithm. However, the matrix provided does not seem complete as a matrix should have a specific number of rows and columns. Typically, a 2x2 matrix would look like this:
| a b |
| c d |
To calculate its inverse, if it exists, you would use the following formula:
1
--------- | d -b |
ad - bc | -c a |
Inversion means you're finding a matrix that, when multiplied by the original matrix, yields the identity matrix. Now, if 'ad - bc' (known as the determinant) is not zero, the inverse exists and the formula above applies. If the determinant is zero, the matrix does not have an inverse. The values mentioned in Table A.1 and the information about reciprocals suggest familiarity with finding inverses of individual numbers, which aligns with the concept of matrix inversion.