Question

For a matrix $A$,

$\alpha \left(\beta A\right)=$

(where $\alpha$ and $\beta$ are real numbers)

• A. $\left(\alpha \beta \right)A$
• B. $\beta \left(\alpha A\right)$
• C. ${\alpha }^{2}A$
• D. ${\beta }^{2}A$

Answer 1

Answer: (A), (B)

The correct options are
A $\left(\alpha \beta \right)A$
B $\beta \left(\alpha A\right)$

For a matrix $A$, $\alpha \left(\beta A\right)$

$\because \alpha$ and $\beta$ are constants, there wont be any change if $\alpha$ is multiplied first or $\beta$ is multiplied.

$\Rightarrow \alpha \left(\beta a\right)=\beta \left(\alpha A\right)$

Also first $\alpha$ and $\beta$ can be multiplied to each other and then $\left(\alpha \beta \right)$ together can be multiplied to $A$.

i.e.,$\alpha \left(\beta a\right)=\beta \left(\alpha A\right)=\left(\alpha \beta \right)A$

$\therefore$Option A and B are correct.

Option C and D are correct if and only if $\alpha$ and $\beta$ are equal.