Answer
a. True.
b. False.
Work Step by Step
a. The definition on page 167 defines determinants recursively, and the statement directly above that definition confirms our answer.
b. From the bottom of page 167, we see that this statement has two problems. First, a cofactor is not a matrix, but the determinant of a matrix. Second, the cofactor is always signed ($+$ or $-$) according to whether $i+j$ is even or odd. The definition given in this statement is of the minor of a matrix entry, not the cofactor.
