Let A = [aij] and B = [bij] be two square matrices of order n and det(A) denote the determinant of A. Then, which of the following is not correct:

Let A = [aij] and B = [bij] be two square matrices of order n and det(A) denote the determinant of A. Then, which of the following is not correct: Correct Answer det(cA) = c [det(A)].

Concept:

Properties of determinants:

• The determinant of a diagonal matrix is the product of the diagonal entries.
• If A and B are both n×n matrices, then det(AB) = det(A) det(B).
• For a n×n matrix A, det(kA) = kⁿ det(A).

• The determinant of a square matrix is the same as the determinant of its transpose.

Calculation:

From the properties of determinants stated above, it can be seen that det(cA) = c is not correct.

The correct statement would be det(cA) = cⁿ .