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How to solve the determinant with all A's on the diagonal, 1 on both ends of the auxiliary diagonal, and all other zeros?
As shown in the figure:

The following is an introduction to the diagonal:

Diagonal, a geometric term, is defined as a line segment connecting any two nonadjacent vertices of a polygon, or a line segment connecting any two vertices of a polyhedron that are not on the same plane. In addition, in algebra, n-order determinant, the numbers from upper left to lower right belong to the main diagonal, and the numbers from upper left to upper right belong to the sub-diagonal. The word "diagonal" comes from the relationship between "angle" and "angle" in ancient Greek, and was later drawn into Latin ("diagonal").

Cramer's law: multiply the numbers of the main diagonal separately, and the values obtained are added; The numbers of the sub-diagonal are multiplied separately, and the opposite numbers of the obtained values are added. The sum of the two is the value of determinant. This method is only applicable to determinant with order less than 4.

The position, shape and size of a triangle can be determined by its three vertices. When there is no given vertex, the shape and size of the triangle can also be determined by some elements of the triangle (* * * six elements, that is, three sides and three internal angles of the triangle).

Refer to Baidu Encyclopedia-Diagonal for the above information.