Identity matrix

1. 4.6 IDENTITY MATRIX LOH HUI YI CHANG WAN LING LEE CHAI EN KAM SIEW HUEY

2. D efinition An identity matrix, I, is a matrix which when multiplying it to another matrix, such as A, the product is the matrix A itself. IA = A and AI = A AI = IA = A

3. Identity Matrix is also called as Unit Matrix or Elementary Matrix. Identity Matrix is denoted with the letter “ I n×n ”, where n×n represents the order of the matrix. One of the important properties of identity matrix is: A×I n×n  = A, where A is any square matrix of order n×n .

4.   A matrix with the same number of rows and columns is called a square matrix. 3x3

5. 1 0 0 0 1 0 0 0 1 An identity matrix, I, is a square matrix and the elements are 0 and 1 only. The elements in the main diagonal are 1 while the others are 0. I = 3 x 3

6. EXAMPLE 1 1 2 1 1 3 7 3 4 1 1    3 7 so 1 1   1 1 is not an identity matrix

7. EXAMPLE 2 1 2 1 0 1 2 3 4 0 1   3 4 so   1 0 0 1   is the identity for 2x2 matrices

8. EXERCISES 1 1 2 1 0 -2 1 0 1 2 1 0 1 2 0 1 -2 1 2 -2 1 2 -2 1

9. -4 -3 If M =  -6 5 ,then find M×I, where I is an identity matrix.

10. Solution: Step 1:  M =  -4 -3  (Given) -6 5 Step 2:  As M is square matrix of order 2×2, the identity matrix I is also of same order 2×2. (Rule for Matrix Multiplication) Step 3:  Then M×I =  -4 -3 1 0                 -6 5 0 1 = (-4x1)+(-3x0) (-4x0)+(-3x1) (-6x1)+(5x0) (-6x0)+(5x1) (Matrix Multiplication) ×

11. Step 4:  =   -4 -3 -6 5 (Simplifying) Step 5:  Hence M×I = M =  -4 -3 -6 5 #