Question

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.

Answer 1

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.

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

Similarly TS also comes out to be:

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

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.

Answer 2

Answer:

Matrices S and T are inverses of each other because ST = TS = I.

Step-by-step explanation:

Option 2