There exists a 2 × 3 matrix A and a 3 × 2 matrix B such that the product AB is invertible. (T/F)
False
False.
In order for the product AB to be invertible, both matrices A and B must be square matrices (having the same number of rows and columns) and their product must have a non-zero determinant. However, in this case, matrix A is a 2 × 3 matrix (2 rows and 3 columns) while matrix B is a 3 × 2 matrix (3 rows and 2 columns). Since neither A nor B is a square matrix, their product AB cannot be invertible.
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