The document introduces identity matrices and provides examples. An identity matrix when multiplied to another matrix A produces the original matrix A. The identity matrix for a matrix of size n x n would be an n x n matrix with 1s along the main diagonal and 0s elsewhere. Two examples are provided to show that when a matrix B is multiplied to a matrix A and A is multiplied to B, the results are the same as the original matrix A, proving that B is an identity matrix.

1. GROUP 5 4.6 IDENTITY MATRIX Leader Name LO SHUI SHUANG Team Name TEO SIANG YING LIM WEN HUI CHAI CHONG LI

2. INTRODUCE AN identity matrix , which when multiplying it to another matrix ,such as A ,the product is the matrix A itself . (n x 1 = 1 x n = n ( n is any number ) There are matrix that works exactly like 1. Such matrix is called an identity matrix . I A = A And A I = A

3. EXAMPLE Given A = 3 4 And B= 1 0 2 -1 0 1 AB = 3 4 1 0 BA = 1 0 3 4 2 -1 0 1 0 1 2 -1 = 3 4 = 3 4 2 -1 2 -1 We find that AB =BA =A. Therefore, B is an identity matrix .

4. 4.6 A Determing Wheather a given Identity Matrix Example Determine whether matrix C is an identity matrix . C = 1 0 , D = 7 5 0 1 4 1 CD = 1 0 7 5 DC = 7 5 1 0 0 1 4 1 4 1 0 1 = 1 x 7 + 0 x 4 1 x 5 + 0 x 1 = 7 x 1 + 5 x 0 7 x 0 + 5 x 1 0 x 7 + 1 x 4 0 x 7 + 1 x 1 4 x 1 + 1 x 0 4 x 0 + 1 x 1 = 7 5 = 7 5 4 1 4 1 = D = D

5. 4.6 B Writing an Identity Matrix and Doing Calculation involving Identity Matrices Example Given D = 4 3 E = 1 0 2 -1 0 1 ED = 1 0 4 3 0 1 2 -1 = 1 x 4 + 0 x 2 1 x 3 + 0 x (-1) 0 x 4 + 1 x 2 0 x 3 + 1 x (-1) = 4 3 2 -1

6. Exercise 4.6 A 1 . Given that A = 1 0 and B = 3 -6 0 1 5 0 Find AB and BA. Is A AN IDENTITY MATRIX ? Exercise 4.6 B 1 . Calculate 6 -7 2 -2 1 0 5 -3 6 -1 0 1