If
is a square invertible matrix, then
is an invertible matrix for every positive integer

, with

Question

If 
  is a square invertible matrix, then 
  is an invertible matrix for every positive integer 
  
, with

Quizplus · Accepted Answer

The given matrix is a square invertible matrix, which means its determinant is non-zero. Therefore, it is guaranteed that its minor matrices are also non-zero. Using the formula for the determinant of a 3x3 matrix, we can see that the determinant of the new matrix can be written as a linear combination of the determinants of its minor matrices, which are non-zero. Thus, the determinant of the new matrix is also non-zero, and hence it is invertible.

If Is a Square Invertible Matrix, Then