The matrix A and B are equivalent. Find out whether the determinants of a and B are equal

The matrix A and B are equivalent. Find out whether the determinants of a and B are equal

The determinant difference of equivalent square matrix of the same order is a nonzero multiple
That is, the existential number k ≠ 0, | a | = k | B |
Not necessarily equal

Equivalent matrix and its determinant
B. Then | a | = | B |; and "the matrices before and after elementary transformation are equivalent, but their determinants are not necessarily equal"

The matrices before and after elementary transformation are equivalent, but their determinants are not necessarily equal. This is right
An equivalent transformation is to multiply a row of a matrix by a non-zero number K. The resulting matrix is equivalent to the original matrix, but the determinant must be changed

If the rank of n × n matrix is n, then at most several of its n-1 subformulas have determinants equal to 0. Why?

The N-1 subexpressions of the same row (column) cannot be all zero
So at most, n ^ 2-N is equal to 0