Lesson Vocabulary

• square matrix
• multiplicative identity matrix
• multiplicative inverse matrix
• determinant
• singular matrix

Take Note Key Concepts: Identity and Multiplicative Inverse Matrices

For an n × n n times n  matrix, the multiplicative identity matrix is an n × n n times n  matrix I, or I n , i sub n , comma  with 1's along the main diagonal and 0's elsewhere.

I 2 = [ 1 0 0 1 ] , I 3 = [ 1 0 0 0 1 0 0 0 1 ] , i sub 2 , equals . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 0 , row2 column 1 , 0 , column 2 1 , end matrix . comma . i sub 3 , equals . matrix with 3 rows and 3 columns , row1 column 1 , 1 , column 2 0 , column 3 0 , row2 column 1 , 0 , column 2 1 , column 3 0 , row3 column 1 , 0 , column 2 0 , column 3 1 , end matrix . comma  and so forth.

If A and B are square matrices and A B = B A = I , eh b equals b eh equals i comma then B is the multiplicative inverse matrix of A, written A − 1 . eh super negative 1 end super , .