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I attached the problem.
I only need help with part b), I provided part a) just to remind you guys what a orthogonal matrix was.
The only 2x2 matrix I can think of with a determinant of + or  1 is something like
√1 0
0 1
The determinant of this would be √1 = + or  1
The second part asks me to show that this matrix is not orthogonal thus A^1≠A^T
A^T=
√1 0
0 1
To calculate A^1 I set up the 2x2 matrix with the identify matrix on the right and reduce so the left becomes the I matrix.
√1 0 1 0
0 1 0 1
→
1 0 1/√1 0
0 1 0 1
But when I do this I get A^1 =
1/√1 0
0 1
Is this still considered = to A^T =
√1 0
0 1
?
I only need help with part b), I provided part a) just to remind you guys what a orthogonal matrix was.
The only 2x2 matrix I can think of with a determinant of + or  1 is something like
√1 0
0 1
The determinant of this would be √1 = + or  1
The second part asks me to show that this matrix is not orthogonal thus A^1≠A^T
A^T=
√1 0
0 1
To calculate A^1 I set up the 2x2 matrix with the identify matrix on the right and reduce so the left becomes the I matrix.
√1 0 1 0
0 1 0 1
→
1 0 1/√1 0
0 1 0 1
But when I do this I get A^1 =
1/√1 0
0 1
Is this still considered = to A^T =
√1 0
0 1
?
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