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        Q. Let A be a 2x3 matrix whereas B be a 3x2 matrix. If det(AB) = 4, then the value of det(BA) is ?(Ans: 0) I tried this problem by taking 2 to 3 examples which satisfy the conditions in the questions and got the answer. But I am not finding a suitable method or any theorem that can be applied.
one year ago

Harsh Patodia
IIT Roorkee
800 Points
										As such there is no theorem for this. Its best to take examples.

one year ago
mycroft holmes
271 Points
										Let $X = \begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}$ Since A is a 2X3 matrix, the equation AX = 0 has a non-trivial solution. and hence the equation (BA) X = 0 has a non-trivial solution, with BA being a 3X3 matrix. Hence, BA is not invertible, i.e. det (BA) = 0

one year ago
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