Asked by Bob
Find all $2 \times 2$ matrices $\bold{A}$ that have the property that for any $2 \times 2$ matrix $\bold{B}$,
\[\bold{A} \bold{B} = \bold{B} \bold{A}.\]
\[\bold{A} \bold{B} = \bold{B} \bold{A}.\]
Answers
Answered by
Steve
Recall that Matrix multiplication is always commutative if ...
... one matrix is the Identity matrix.
... one matrix is the Zero matrix.
... both matrices are 2×2 rotation matrices. (basically case #2)
... both matrices are Diagonal matrices.
... one matrix is the Identity matrix.
... one matrix is the Zero matrix.
... both matrices are 2×2 rotation matrices. (basically case #2)
... both matrices are Diagonal matrices.
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