Question

Please help! Correct answer only, please! Consider the matrix shown below: Find the inverse of the matrix A: (i.e Find A^-1).

Answer 1

Answer: A

Step-by-step explanation:

Formula for inverse of a matrix is:

$A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\qquad \rightarrow \qquad A^{-1}=\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]$

$A=\left[\begin{array}{cc}2&5\\3&8\end{array}\right] \qquad \rightarrow \qquad A^{-1}=\dfrac{1}{2(8)-5(3)}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\dfrac{1}{1}\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]\\\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \quad =\left[\begin{array}{cc}8&-5\\-3&2\end{array}\right]$

Answer 2

We have that  Option A is the correct option as its the correct in verse of the Matrix A

From the question we are told that:

$A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}$

Inverse of a Matrix

The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is A^{-1}, and A.A^{-1} = I.

Therefore the inverse of the Matrix A is

$A= \begin{vmatrix}2 & 5 \\3 & 8\end{vmatrix}$

Giving

$A^{-1}= \begin{vmatrix}8 & -5 \\-3 & -2\end{vmatrix}$

In conclusion

The correct Option is Option A as its the correct in verse of the Matrix A

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In conclusion