Given matrices S and T below, which statement is true?Matrices S and T are not inverses of each other because S+T mc016-3.jpg I.Matrices S and T are inverses of each other because ST = TS = I.Matrices S and T are inverses of each other because the determinant of S is 1.Matrices S and T are not inverses of each other because the determinant of S equals the determinant of T.

Two matrices are inverse of each other if and only if the product of two matrices is an Identity matrix.

So, in order to find if S and T are inverse of each other, we have to show that 

ST = TS = I 

where I is the identity matrix of order 2 x 2.

[tex]ST= \left[\begin{array}{cc}4&11\\-3&-8\end{array}\right] \left[\begin{array}{cc}-8&-11\\3&4\end{array}\right] \\ \\ ST=\left[\begin{array}{cc}4(-8)+11(3)&4(-11)+11(4)\\-3(-8)+(-8)(3)&-3(-11)+(-8)(4)\end{array}\right] \\ \\ ST=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

Similarly TS also comes out to be:

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

Since TS is equal to ST and both are equal to the Identity matrix, we can conclude that S and T are the inverse of each other and therefore, option B is the correct answer.