True or False determine whether each statement is true or fa

True or False? determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. (a) The determinant of a 2 times 2 matrix A is a_21a_12 - a_11a22 (b) The determinant of a matrix of order 1 is the entry of the matrix. (c) The ij-cofactor of a square matrix A is the matrix defined by deleting the ith row and jth column of A.

Solution

(a). The statement is false. The value of the determinant is –(a₂₁a₁₂-a₁₁ a₂₂).

(b). The statement is false. The ijth minor M _ij of a square matrix A is the determinant defined by deleting the ith row and the jth column of A. The cofactor of an element a_ij of a matrix A, written as C_ij is defined as (1)^i+j M_ij.