If A and B are square matrices of order 3, then the true statement is/are (where I is unit matrix).<br>(A) det (-A) = -det A<br>(B) If AB is singular then atleast one of A or B is singular<br>(C) det (A + I) = 1 + det A<br>(D) det (2A) = 2^3 det A
Step-by-Step Solution
Key Concept: Properties of determinants: det(kA) = k^n det(A) for order n, det(AB) = det(A)det(B), and det(-A) = (-1)^n det(A).
For a 3x3 matrix A:<br>(A) det(-A) = (-1)^3 det(A) = -det(A). This is true.<br>(B) det(AB) = det(A)det(B). If AB is singular, det(AB) = 0, so det(A)det(B) = 0, meaning at least one of det(A) or det(B) is 0. This is true.<br>(C) det(A+I) is not generally equal to 1 + det(A). This is false.<br>(D) det(2A) = 2^3 det(A) = 8 det(A). This is true.
Correct Answer: 1, 2, 4