This is maths matrices top question

The product AB is [tex]AB = \left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
The product BA is [tex]BA = \left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
Matrices A and B are inverse matrices

The matrices are given as:

[tex]A = \left[\begin{array}{cc}2&3\\5&8\end{array}\right][/tex] and [tex]B = \left[\begin{array}{cc}8&-3\\-5&2\end{array}\right][/tex]

The product AB is calculated as:

[tex]AB = \left[\begin{array}{cc}2*8-3*5&-2*3+3*2\\5*8-8*5&-5*3+8*2\end{array}\right][/tex]

Evaluate the products

[tex]AB = \left[\begin{array}{cc}16-15&-6+6\\40 -40&-15+16\end{array}\right][/tex]

Evaluate the differences

[tex]AB = \left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

The product BA is calculated as:

[tex]BA = \left[\begin{array}{cc}8*2-3*5&8*3-3*8\\-5*2+2*5&-3*5+2*8\end{array}\right][/tex]

Evaluate the products

[tex]BA = \left[\begin{array}{cc}16-15&24-24\\-10+10&-15+16\end{array}\right][/tex]

Evaluate the differences

[tex]BA = \left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

In the above computations, we have:

[tex]AB = \left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex] and [tex]BA = \left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

Also, the elements of the principal diagonal of AB and BA are 1, while other elements are 0.

This means that matrices A and B are inverse matrices