Question

Give examples of two non zero 3×3 matrices a and b such that ab = 0.

A. in your example in a, is ba = 0?
B. is it always true that ba = 0?
C. is your a2 = 0? 1

Answer 1

Two examples of non-zero 3x3 matrices a and b such that ab = 0 are provided. It is shown that ba is not necessarily equal to 0 and a^2 is not equal to the zero matrix.

Step-by-step explanation:

To find two non-zero 3x3 matrices a and b such that ab = 0, we can use the following examples:

Example 1:

a = [1 0 0; 0 0 0; 0 0 0]

b = [0 0 0; 1 0 0; 0 0 0]

Example 2:

a = [0 0 0; 0 1 0; 0 0 0]

b = [0 0 0; 0 0 0; 0 0 1]

In both examples, a multiplied by b equals the zero matrix. However, in Example 1, b multiplied by a is not equal to the zero matrix, while in Example 2, b multiplied by a is also equal to the zero matrix.

So, the answer to part A is no, ba is not equal to zero in both examples.

For part B, it is not always true that ba = 0. The examples provided demonstrate this.

In both examples, a^2 is not equal to the zero matrix.