Let a and b be n x n matrices.

the determinant of a is the product of the diagonal entries in a. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a.

the statement is true because the determinant of any triangular matrix a is the product of the entries on the main diagonal of a.

b.

the statement is false because the determinant of the 2×2 matrix a = __ is not equal to the product of the entries on the main diagonal of a.

(type an integer or simplified fraction for each matrixelement.)

c.

the statement is true because the determinant of any square matrix a is the product of the entries on the main diagonal of a.

The statement is FALSE, option B is correct

Step-by-step explanation:

What option A says is true, the determinant of any triangular matrix A is the product of the entries on the main diagonal of A.

However, it is not stated that A is triangular, so this afirmation is not enough to prove that det(A) is the product of the diagonal elements in A. So we cant count on option A.

Option C is not valid, and the argument is based on a wrong claim. The product of the entries of the main diagonal of a matrix A isnt necessarily det(A). However, the claim is true when A is traingular, as option A states.

Option B is the correct one, the 2x2 matrix   has determinant equal to 0, because it has  2 equal rows. However the product of the elements of the diagonal gives 1, so the product of the entries of the diagonal of A isnt equal to det(A).

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step-by-step explanation:

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