Based on the matrices given, the true statement on matrices AB = BA is A. A⁻¹ = ¹/₃B.
What is true on AB = BA?
If:
AB = BA = [3 0]
[0 3]
Then:
AB = BA = 3 [1 0]
[0 1]
This can be further written as:
AB = BA = 3I₂
And again as:
A (¹/₃ B) = I
This then allows us to either write this as:
A⁻¹ = ¹/₃ B
Or:
B⁻¹ = ¹/₃ A
In conclusion, option A is correct.
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