Discussion
If A and B are both non-singular n×n matrices, then which of the following statement is NOT TRUE. Note: det represents the determinant of a matrix.
Answer: B
The statement that is NOT TRUE is det(A+B) = det(A) + det(B).
The determinant is multiplicative, not additive. A quick counterexample: take A = B = I, the 2 × 2 identity. Then det(A + B) = det(2I) = 4, but det(A) + det(B) = 1 + 1 = 2.
The other three are standard properties. det(AB) = det(A)det(B) for square matrices. Since AA-1 = I, its determinant is 1. And a matrix and its transpose have the same determinant.
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