In the general examination, the simplest method of inverse matrix is to use augmented matrix.

If the inverse matrix needs to be

Then, elementary row transformation is performed on the augmented matrix (A E), where E is identity matrix.

Transform a into e, and the inverse of this matrix is the matrix of the original position of e.

The principle is that the inverse of a is multiplied by (AE) = (AE inverse). Elementary row transformation is obtained by multiplying the inverse matrix of a on the left side of the matrix.

As for the special ... the inverse of the diagonal matrix is a diagonal matrix with the reciprocal of the diagonal element as the diagonal element.

The rest can only be qualitative, for example, the inverse of the upper triangular matrix must be the upper triangle, and so on.

You won't be asked to calculate too many matrices during the exam.