If a and B are square matrices of same order such that `AB+BA=O`, then prove that `A^(3)-B^(3)=(A+B) (A^(2)-AB-B^(2))`.

Explanation

To prove that \( A^3 - B^3 = (A + B)(A^2 - AB - B^2) \) given that \( AB + BA = O \) (where \( O \) is the zero matrix), we can follow these steps:

### Step 1: Start with the left-hand side (LHS)
We begin with the expression \( A^3 - B^3 \).

### Step 2: Factor the left-hand side
We can use the identity for the difference of cubes:
\[
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