First, to judge a positive definite matrix, we need to know all the principal components of its sequence.

If all the major subsequences of a sequence are greater than 0, it is a positive definite matrix.

And in this problem | a | =-a 2-b 2 =- 1

Explain that it is not a positive definite matrix.

For a negative definite matrix, the ordinal number of odd order is mainly negative, and the ordinal number of even order is mainly positive.

Therefore, it is obvious that matrix A is not a negative definite matrix.

For elementary matrix, identity matrix is obtained after basic elementary transformation. Obviously, it is impossible for identity matrix to get the matrix A through a basic elementary transformation.

For orthogonal matrices, each column is an orthogonal vector.

You see, the inner product of the first column (a, b) and the second column (b, -a) is zero, indicating that these two vectors are orthogonal.

So this matrix is orthogonal.

The fourth question

First of all, the nature of what I learned is what the teacher said (I am not a math major, so I may not learn much), and some of it has not been proved.

I tell you these attributes. If you want to prove them, you can search online.

Eigenvalues can be equal; The characteristic value can be 0; The product of eigenvalues is the value of matrix determinant; The sum of eigenvalues is equal to the trace of matrix (the trace of matrix is the sum of elements on the diagonal of matrix)