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Question: For A = \(\begin{bmatrix} 4 & 2i \\ i & 1 \end{bmatrix}\), (A – 2I) (A – 3I) is a –...

For A = [42ii1]\begin{bmatrix} 4 & 2i \\ i & 1 \end{bmatrix}, (A – 2I) (A – 3I) is a –

A

Null matrix

B

Orthogonal matrix

C

Unit matrix

D

Diagonal matrix

Answer

Null matrix

Explanation

Solution

[22ii−1]\begin{bmatrix} 2 & 2i \\ i & - 1 \end{bmatrix} [12ii−2]\begin{bmatrix} 1 & 2i \\ i & - 2 \end{bmatrix}= [0000]\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}