Question

For any square matrix A,if A²-3A+4i=0 then A−1=...........

Answer 1

Answer:

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Step-by-step explanation:KZLJXKCJUDSUL

Answer 2

$A^{-1}$ = $\left[\begin{array}{ccc}-1/2&1/4\\-1/2&-1/4} \\\end{array}\right]$

Given:

For a square matrix A, A²-3A+4i=0

To Find:

The value of $A^{-1}$ from the given question

Solution:

(A²-3A+4i) $A^{-1}$ = O$A^{-1}$

A(AA^-1) + 3I +4$A^{-1}$ = O

A + 3I  +4$A^{-1}$ = O

4$A^{-1}$ = -A-3I+O

$A^{-1}$ = 1/4{ -A-3I}]

$A^{-1}$ = $\frac{1}{4}$ $\left[\begin{array}{ccc}1-3&1+0\\-2+0&2-3} \\\end{array}\right]$

$A^{-1}$ = $\left[\begin{array}{ccc}-1/2&1/4\\-1/2&-1/4} \\\end{array}\right]$

Hence, we get the value of $A^{-1}$ =  $\left[\begin{array}{ccc}-1/2&1/4\\-1/2&-1/4} \\\end{array}\right]$

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