Question

If A′ is the transpose of a square matrix A, then

(A) |A| ≠ |A′|

(B) |A| = |A′|

(C) |A| + |A′| = 0

(D) |A| = |A′| only when A is symmetric 

Answer 1

Answer is (B) |A| = |A′|

A = A′. Then |A| = |A′| because the expansion of a determinant row-wise is same as the expansion of a determinant column wise.