Determine whether the statement is true or false and circle

Determine whether the statement is true or false, and circle the correct answer. Each question is worth If AB = 0, then either A = 0 or B = 0. T F If A and B are n times n, then det AB = det BA. T F If A and B are m times n, then both AB^T and A^T B are defined. T F Any system of n linear equations in n variables can be solved by Cramer\'s rule. T F If A is a 2 times 2 matrix, then det(5A) = 5 det A. T F If A is a 3 times 3 matrix with three pivot positions, there exist elementary matrices E_1, ..., E_p such that E_p ... E_1 A = I. T F If AB = I, then A is invertible. Y F If A is a 2 times 2 matrix with a zero determinant, then one column of A is a multiple of the other. T F If A is n times n and det A = 2, then det(A^3) = 6. T F If A and B are n times n, then (A - B) (A + B) = A^2 - B^2. T F

Solution

1) True

2) True as it is square matrix

5) True as the matrix is a square matrix