A square matrix of order n is similar to a diagonal matrix A. the order of a square matrix A is equal to N, right

A square matrix of order n is similar to a diagonal matrix A. the order of a square matrix A is equal to N, right

incorrect.
Similar matrices have the same rank
The rank of a is equal to the number of nonzero elements on the main diagonal of that diagonal matrix

What is the eigenvalue of n-order square matrix with the same value on the main diagonal and other values
The value on the main diagonal is a, the other values are B, and the order is n
Represented by a, B and n

For this kind of determinant C: add to the first column from the second column to the nth column, and then subtract the first row from the second row to the nth row, we can see that the determinant is (a + (n -- 1) b) (a -- B) ^ (n -- 1). Note that AE -- C is still this kind of determinant, so | AE -- C | = (a -- a -- (n -- 1) b) (a -- A + b) ^ (n -- 1)

If a and B matrices of order n are equivalent, are their determinants equal

Two equivalent matrices A and B of order n
Their determinants differ by a nonzero constant multiple, which is not necessarily equal
If a and B are equivalent, there exists an invertible matrix P and Q satisfying PAQ = B
Take the determinant on both sides to get | P | a | Q | = | B|
Let k = | P | Q |, then K ≠ 0, and | B | = k | a |