Question

if A = [2 -3 x y] and A²=I where I is a unit matrix of order 2*2 value of x y​

Answer 1

Answer:

x=1 and y= -2

Step-by-step explanation:

$A= \left[\begin{array}{ccc}2&-3\\x&y\end{array}\right] \\\\A^{2} = A*A = I = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

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

$A^{2}= \left[\begin{array}{ccc}2&-3\\x&y\end{array}\right] \left[\begin{array}{ccc}2&-3\\x&y\end{array}\right] =\left[\begin{array}{ccc}4-3x&-6-3y\\2x+xy&-3x+y^2\end{array}\right]=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Now comparing coefficients,

$\left[\begin{array}{ccc}4-3x&-6-3y\\2x+xy&-3x+y^2\end{array}\right]=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

4 - 3x = 1

3 = 3x

x=1

-6-3y=0

3y=-6

y= -2

HOPE IT HELPS!

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