True False. If A is 3x3 and det(A) = 2, then det(A³) = 6.

True False. If A is row equivalent to B, then det A = det B.

True False. det (A^TA) is always greater than or equal to 0.

True False. If A, B and C are nonzero 2×2 matrices such that AB=AC, then B=C.

True False. For all 5x5 matrices B and C, det (BC) = det (CB).

True False. If B is row equivalent to a nonsingular matrix, then det (B) is nonzero.

True False. If E is a type I elementary matrix, then det (E) = 1.

True False. If A³ = O, then det(A)=0.

True False. Every square matrix is row equivalent to either the identity or to a matrix that contains a row of zeroes.

True False. If A is 3x3 then det(5A) = 5det(A).

Written by S.Hudson.