Chapter 3.CR, Problem 75CR

To determine

(a)

Whether the given statement “the co-factor of $C_{22}$ is always a positive integer” is true or false.

To determine

(b)

Whether “If a square matrix $B$ is obtained from matrix $A$ by interchanging the rows, then $\det \left(B\right)=\det \left(A\right)$” is true or false.

To determine

(c)

Whether “If one column of a square matrix is a multiple of another column, then the determinant is zero” is true or false.

To determine

(d)

Whether the given statement “If $A$ is a square matrix then $\det \left(A\right)=-\det \left(A^T\right)$” is true or false.