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Use the above equalities (and some arithmetic) to conclude that: Can you show that the determinant Now, ignoring the formulae for a moment and instead thinking about the definition of det (A) as the signed volume of the parallelopiped formed by the columns of A, can you argue that the determinant of a diagonal matrix is the product of its diagonal entries? Can you also argue that the determinant of a triangular matrix is the product of its diagonal entries. In other words, can you show that can you explain why det (AB) = det (A) det (B). whenever A and B are matrices that are 'compatible' (with respect to matrix multiplication). Can you explain why the following row-operation: "add 3 times the first row of A to the third row of A" corresponds to the following matrix multiplication: Can you explain why the following column-operation "add twice the second column of A to the third column of A" corresponds to the following matrix multiplication