Q:

Given matrices S and T below, which statement is true?S=( 4 11 -3 -8)T=(-8 -11 3 4)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.

Accepted Solution

A:
The matrices are
S =(4 11                           T= ( -8 11
      -3  -8)                                 3  4 )
Inverse of a matrix is a matrix derived from another matrix such that if you pre- multiply it with the original matrix you get a unit matrix.
if we multiply S and T
 ST will be 
        ( 4 11    ×      (-8 11   = ( 1 0
          -3 -8)           -3 -4)         0 1)
and also TS
          ( -8 11      ×     (4 11  = ( 1 0
             -3 -4)            -3 -8)       0 1)
therefore, matrices S and T are inverses of each other because ST = TS= I 



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