Further Maths Textbook

Study Notes (Inverse Matrix)

Identity Matrix

Square matrix (n × n),  every element is 0, except 1s line up from top left corner to the right bottom corner shown below.

 

Ex. 1

Prove that in any (2 × 2) matrix A to satisfy AI = IA = A, I is (2 × 2) identical matrix.

Solution

To prove general facts, it is good to let a matrix (fact) be a general expression, here using letters, a, b, c and d

 

N.B:  Of course this rule AI = IA = A can be extended to n × n matrix, as we do not prove here.

 

Practice 1

Prove that the following matrix satisfies the equation AI = IA = A.

Solution

 

Study Notes

The matrix X to satisfy AX = XA = I , X is called inverse matrix expressed as A–1

In other words A A–1 = A–1A = I (Identical Matrix)