The determinant of an n×n matrix A is the product of the diagonal entries in A.A. TrueB. False

To determine if the statement is true or false, we need to consider the definition of the determinant of an n×n matrix A.

Step 1: Recall that the determinant of a 1×1 matrix is simply the entry in the matrix.

Step 2: For a 2×2 matrix A = [a b; c d], the determinant is calculated as ad - bc.

Step 3: For larger matrices, the determinant can be found using various methods such as cofactor expansion or row operations. However, one important property is that the determinant is the product of the diagonal entries in the matrix when it is in upper triangular form.

Step 4: Therefore, the statement "The determinant of an n×n matrix A is the product of the diagonal entries in A" is FALSE. The determinant is not always equal to the product of the diagonal entries, but rather depends on the specific properties and values of the matrix.