First slide

Operations of matrix

Question

If A and B are two square matrices of the same size, then $(A + B)^{2} = A^{2} + 2 A B + B^{2}$ can hold if and only if

Easy

A

$A B = B A$
B

$A B + B A = O$
C

$| A B | \neq 0$
D

$| A B | = 0$

Solution

$(A + B)^{2} = (A + B) (A + B) = A^{2} + B A + A B + B^{2}$
$∴ (A + B)^{2} = A^{2} + 2 A B + B^{2}$ if and only if $A B = B A$

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