First slide

Operations of matrix

Question

Let A, B be two 3 × 3 matrices with entries from real numbers. Which one of the following is true?

Easy

A

$(A + B)^{3} = A^{3} + 3 A^{2} B + 3 A B^{2} + B^{3}$
B

$(A B)^{2} = O \Rightarrow A B = O$
C

$(A + B) (A - B) = A^{2} - B^{2}$
D

$(A + B) A = B A + A^{2}$

Solution

(a), (b), (c) cannot hold in general unless $A B = B A$

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