If A= [ rr 4 & -1 2 & 1 ], then (A+2 I)(A-3 I) is equal to: - Vidyadip

MCQ

If $A=\left[\begin{array}{rr}4 & -1 \\ 2 & 1\end{array}\right]$, then $(A+2 I)(A-3 I)$ is equal to:

✓
$\left[\begin{array}{ll}4 & -4 \\ 8 & -8\end{array}\right]$
B
$\left[\begin{array}{rr}4 & 8 \\ -4 & -8\end{array}\right]$
C
$\left[\begin{array}{ll}-4 & 4 \\ -8 & 8\end{array}\right]$
D
$\left[\begin{array}{rr}-4 & 4 \\ 8 & -8\end{array}\right]$

✓

Answer

Correct option: A.

$\left[\begin{array}{ll}4 & -4 \\ 8 & -8\end{array}\right]$

(a) $\left[\begin{array}{ll}4 & -4 \\ 8 & -8\end{array}\right]$
Explanation:
(A+2 I)(A-3 I)
$=\left\{\left[\begin{array}{rr}4 & -1 \\ 2 & 1\end{array}\right]+2\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\right\}$
$\left\{\left[\begin{array}{rr}4 & -1 \\ 2 & 1\end{array}\right]-3\left[\begin{array}{rr}1 & 0 \\ 0 & 1\end{array}\right]\right\}$
$\begin{array}{l}=\left[\begin{array}{rr}6 & -1 \\ 2 & 3\end{array}\right]\left[\begin{array}{rr}1 & -1 \\ 2 & -2\end{array}\right] \\ =\left[\begin{array}{rr}6-2 & -6+2 \\ 2+6 & -2-6\end{array}\right] \\ =\left[\begin{array}{rr}4 & -4 \\ 8 & -8\end{array}\right]\end{array}$

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