│A*│ and │A│ is the relationship between?

│A*│=│A│^(n- 1)

Proof: a * = | a | a (- 1)

│A*│=|│A│*A^(- 1)|

│A*│=│A│^(n)*|A^(- 1)|

│A*│=│A│^(n)*|A|^(- 1)

When determinant was first invented, it was used to solve linear equations. Obviously, matrices are used to represent the coefficients of linear equations. According to Wikipedia, the concept of determinant was originally developed with the solution of equations. The original prototype was independently drawn by Japanese mathematician Guan Xiaohe and German mathematician gottfried leibniz almost at the same time. 」

(1) determinant is a function, but this is nonsense-we need to know what its corresponding value is-specifically, the return value of this function is a volume. For example, the determinant of 2×2 is obviously the directed area of a parallelogram. How to understand it depends on Wikipedia. So you can understand why if two rows of determinants are equal, the value is equal to zero, because it can't be opened at all, and the volume is of course zero.

(2) Linear transformation is represented by matrix. Multiplying a matrix with a vector v gives a vector u, which completes the transformation from v to u.