The square matrix a is called orthogonal provided
thatat=a-1. show that the determinant of such
amatrix must be either +1 or -1.

The proof is done below.

Step-by-step explanation:  Given that the square matrix  A is called orthogonal provided that

We are to show that the determinant of such a matrix is either +1 or -1.

We will be using the following result :

Given that, for matrix A,

Taking determinant of the matrices on both sides of the above equation, we get

Thus, the determinant of matrix A is either +1 or -1.

Hence showed.

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis