First slide

Operations of matrix

Question

Let $A = (\begin{array}{ll} 1 ââââ 2 \\ 3 ââââ 4 \end{array})$ and $B = (\begin{array}{ll} a ââââ 0 \\ 0 ââââ b \end{array}), a, b â N$

Moderate

A

Then there exists infinitely many Bâs such that AB = BA
B

there cannot exist B such that AB = BA
C

there exist more than one but finite number of Bâs such that AB = BA
D

there exists exactly one B such that AB = BA

Solution

If $b = a, B = a I$ and B commutes with every matrix A.

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