Q91 / 150 · MHT CET 2019 (Shift 2) · Mathematics

If $[\begin{matrix} 1 + 2 i & i \\ - i & 1 - 2 i \end{matrix}]$ where $i = \sqrt{- 1}$ , then A (adj A) = ….

A
-2 $l$
B
2 $l$
C
5 $l$
Correct answer
D
4 $l$

Solution

A = [\begin{matrix} 1 + 2 i & i \\ - i & 1 - 2 i \end{matrix}]

∴ |A| = |\begin{matrix} 1 + 2 i & i \\ - i & 1 - 2 i \end{matrix}| = (1 + 2 i) (1 - 2 i) + i^{2}

= 1 - {(2 i)}^{2} + (- 1) = 1 + 4 - 1 = 4

∴ A (a d j A) = |A| |= 4|

Hence, the correct answer is option: 'D'.

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