Question

Is X=[−14−32] the inverse of A=[15−25310−110]?

Answer 1

Answer:

The product of the matrices is not the identity matrix. Therefore, X and A are not inverses of each other.

Step-by-step explanation:

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Answer 2

The product of the matrices is an identity matrix. Therefore, X and A are inverse of each other.

The matrices are given as:

$X = \left[\begin{array}{cc}-1&-3\\4&2\end{array}\right]$

$A = \left[\begin{array}{cc}\frac 15&\frac 3{10}\\-\frac 25 &-\frac 1{10}\end{array}\right]$

To check the matrices are inverse, we calculate their products.

$A \times X = \left[\begin{array}{cc}\frac 15&\frac 3{10}\\-\frac 25 &-\frac 1{10}\end{array}\right] \times \left[\begin{array}{cc}-1&-3\\4&2\end{array}\right]$

Multiply the rows of A by the column of X.

This gives

$A \times X = \left[\begin{array}{cc}\frac 15 \times -1 + \frac{3}{10} \times 4&\frac 15 \times -3 + \frac{3}{10} \times 2\\ -\frac 25 \times -1 - \frac{1}{10} \times 4&-\frac 25 \times -3 + -\frac{1}{10} \times 2\end{array}\right]$

$A \times X = \left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

The product of  A and X is an identity matrix.

This means that; both matrix are inverse of each other

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