Generally speaking, if A and B are similar matrices, then their reversibility is the same. Because by definition, similar matrices have the same reversibility. So when they meet the invertibility condition, their inverse matrices are similar. Matrix similarity is an equivalent relationship with reflexivity, symmetry and transitivity.

Research on the concept of matrix;

After the study of determinant, matrix officially appeared as the research object of mathematics. Logically, the concept of matrix precedes determinant, but in actual history it is just the opposite.

Japanese mathematician Guan Xiaohe (1683) and Gottfried Wilhelm Leibniz (1693), one of the discoverers of calculus, established determinant theory almost simultaneously. Then the determinant gradually developed into a tool for solving linear equations. 1750, Gabriel Cramer discovered Cramer's law.