Inverse matrix calculation formula: a * = | a | a (- 1), (a *) (- 1) = a/| a |.

Mathematically, m×n matrix is a rectangular array with M rows and N columns. Elements in a matrix can be numbers, symbols or mathematical expressions. Inverse matrix: Let A be an n-order square matrix in the number field. If there is another n-order matrix B in the same number field, let AB = BA = E .. Then we call B the inverse matrix of A and A the invertible matrix.

Formula: the inverse matrix of a = (1| a |) A*, where a * is the adjoint matrix of a.

Elementary transformation method: the block matrix (a, e) is subjected to elementary transformation. When the first half of A is transformed into identity matrix E, the second half of E is transformed into the inverse matrix of A. ..

Guess: If AB=E or BA=E can be obtained through known conditions, then B is the inverse matrix of A. ..

Inverse matrix calculation of second-order square matrix:

A/(ad-bc), let a be an n-order matrix in the number domain. If there is another n-order matrix B in the same number field, so that: AB=BA=E, then we say that B is the inverse matrix of A, and A is called invertible matrix. Note: E is identity matrix.

Second order identity matrix

The second-order identity matrix is a 2×2 matrix, and only the order is defined for the square matrix. In the multiplication of matrices, one matrix plays a special role, just like 1 in the multiplication of numbers. This matrix is called identity matrix, and it is a square. The elements on the diagonal (called the main diagonal) from the upper left corner to the lower right corner are 1. Everything else is 0.

According to the characteristics of identity matrix, any matrix multiplied by identity matrix is equal to itself, and the uniqueness of identity matrix is also widely used in higher mathematics.

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Square array is a kind of formation used by ancient troops in combat, which is to arrange troops in a square formation on an open field. The ancient phalanx consists of the former army, the middle army and the rear army nested with each other. The plane of the phalanx is in the shape of "Hui", which reflects a political and geographical structure in ancient concepts and comes from the world view of "the sky is round and the place is round".