A and B are n x n matrices Check the true statements below I

A and B are n x n matrices. Check the true statements below: If detA is zero, then two rows or two columns are the same, or a row or a column is zero. detA^T = (-1)detA. If two row interchanges are made in sucession, then the determinant of the new matrix is equal to the determinant of the original matrix. The determinant of A is the product of the diagonal entries in A.

Solution

for part a) False. Let

A=[ 2 4, 1 2]
A then det(A) = 0 but no two rows nor two columns are the same,
nor is a row or a column zero. so it is false

For part b) det AT =(-1)det A is FALSE because detAT =det A.

for part c) true

for part d) it is false