Example ¹1. Finding the Inverse of a 2x2 MatrixThis solution has been made using the calculator presented on the site. It is necessary to calculate a matrix A^{1}, inverse to the given one:
Formula for calculating the inverse matrix:
A_{11} ... A_{22} are numbers (algebraic additions) that will be calculated later. It is impossible to divide by zero. Therefore, if the determinant of A is zero, then it is impossible to calculate inverse matrix. Let's calculate the determinant A.
= 1 * 3  2 * 1 = 3  2 = 1
Determinant A is not zero. It is possible to calculate inverse matrix. Let's calculate numbers (algebraic additions) A_{11} ... A_{22}
Result:
It is necessary to check that A^{1} * A = E.
b_{11} = 3 * 1 + ( 2) * 1 =
3  2 = 1
b_{12} = 3 * 2 + ( 2) * 3 =
6  6 = 0
b_{21} = 1 * 1 + 1 * 1 =
1 + 1 = 0
b_{22} = 1 * 2 + 1 * 3 =
2 + 3 = 1
Thus, the found matrix A^{1} is inverse for the given matrix A. © 20102021 If you have any comments, please write to siteReshmat@yandex.ru 
