If A = 1 2 3 - 1 1 2 1 2 4 then A 2 - 5 A A - 1 =

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Question: Answered & Verified by Expert

If

A = [\begin{matrix} 1 & 2 & 3 \\ - 1 & 1 & 2 \\ 1 & 2 & 4 \end{matrix}]

then

(A^{2} - 5 A) A^{- 1} =

MathematicsMatricesMHT CETMHT CET 2018

Options:

A $[\begin{matrix} 4 & 2 & 3 \\ - 1 & 4 & 2 \\ 1 & 2 & 1 \end{matrix}]$
B $[\begin{matrix} - 4 & 2 & 3 \\ - 1 & - 4 & 2 \\ 1 & 2 & - 1 \end{matrix}]$
C $[\begin{matrix} - 4 & - 1 & 1 \\ 2 & - 4 & 2 \\ 3 & 2 & - 1 \end{matrix}]$
D $[\begin{matrix} - 1 & - 2 & 1 \\ 4 & - 2 & - 3 \\ 1 & 4 & - 2 \end{matrix}]$

Solution:

2440 Upvotes Verified Answer

The correct answer is:

[\begin{matrix} - 4 & 2 & 3 \\ - 1 & - 4 & 2 \\ 1 & 2 & - 1 \end{matrix}]

(A^{2} - 5 A) A^{- 1}

= A^{2} \cdot A^{- 1} - 5 A A^{- 1}

= A - 5 I

= [\begin{matrix} 1 & 2 & 3 \\ - 1 & 1 & 2 \\ 1 & 2 & 4 \end{matrix}] - [\begin{matrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{matrix}]

= [\begin{matrix} - 4 & 2 & 3 \\ - 1 & - 4 & 2 \\ 1 & 2 & - 1 \end{matrix}]

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