An Introduction to Inverses (9.9.1)

Question 1

• The multiplicative identity of any number is 1 because when any number multiplies with 1 the product is the number itself.

Answer 1

• The multiplicative identity of any number is 1 because when any number multiplies with 1 the product is the number itself.

Question 2

• The multiplicative inverse of any number is the value that, if you multiply it with the given number, produces 1. Usually this is the reciprocal of the number.

Answer 2

• The multiplicative inverse of any number is the value that, if you multiply it with the given number, produces 1. Usually this is the reciprocal of the number.

Question 3

• The identity matrix is the one that will produce a given matrix when that matrix multiplies with the identity matrix. The identity matrix has the characteristic that all of its terms are 0 except those that lie on the main diagonal from the upper left corner to the lower right corner.

Answer 3

• The identity matrix is the one that will produce a given matrix when that matrix multiplies with the identity matrix. The identity matrix has the characteristic that all of its terms are 0 except those that lie on the main diagonal from the upper left corner to the lower right corner.

Question 4

• The inverse matrix is the one that will produce the identity matrix when multiplied with a given matrix. The only matrices which have inverses are those which are non-singular; i.e. those whose determinants do not equal zero.

Answer 4

• The inverse matrix is the one that will produce the identity matrix when multiplied with a given matrix. The only matrices which have inverses are those which are non-singular; i.e. those whose determinants do not equal zero.