Evaluate A 2 + 2 I if A = 1 0 1 2

Evaluate

A^{2} + 2 I

if

A = [\begin{array}{l} 1 & 0 \\ 1 & 2 \end{array}]

$2 A$
$3 A$
$4 A$
$5 A$

Solution

$A^{2} + 2 I = [\begin{matrix} 1 & 0 \\ 1 & 2 \end{matrix}] [\begin{matrix} 1 & 0 \\ 1 & 2 \end{matrix}] + 2 [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

$= [\begin{matrix} 1 & 0 \\ 3 & 4 \end{matrix}] + [\begin{matrix} 2 & 0 \\ 0 & 2 \end{matrix}]$

$= [\begin{matrix} 3 & 0 \\ 3 & 6 \end{matrix}]$

$= 3 A$

Asked in: AP EAMCET 2020 (23 Sep Shift 1)

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