Linear Algebra: The transpose of A equals Inverse A, so

[jinksys]

If the transpose of A equals the Inverse of A, then det(A)=1.

False. However, I don't follow the logic.

If transA=InverseA, doesn't that mean the matrix is the identity matrix?

The explanation says that det(A)= 1 and -1.

 

[Office_Shredder]

If the transpose of A equals the Inverse of A, then det(A)=1.

False. However, I don't follow the logic.

If transA=InverseA, doesn't that mean the matrix is the identity matrix?

The explanation says that det(A)= 1 and -1.

If the transpose of A is the inverse of A, it does not have to be the identity matrix. All it says is that the columns of A are an orthonormal basis, as are the rows (check this by matrix multiplication).

Examples are rotation matrices, and reflection matrices (try constructing some 2x2 example to be sure).

 

[Hurkyl]

Try looking at a simple case. How about 1x1 matrices? There is only one unknown -- write down the equations that define what it means for the transpose to equal the inverse.

 

[Jakk01]

If you start with det(AA^-1)=det(I) and consider that det(A^T)=det(A) you should be able to work this out.