edited by
3,372 views
8 votes
8 votes

If a square matrix A satisfies $A^TA=I$, then the matrix $A$ is

  1. Idempotent
  2. Symmetric
  3. Orthogonal
  4. Hermitian
edited by

4 Answers

1 votes
1 votes

Idempotent Matrix: $AA=A^2=A$

Symmetric Matrix: $A=A^T$

Orthogonal Matrix: $AA^T = I$ (Option C)

Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose.

 

Bonus:-

Singular Matrix: Matrix whose determinant is 0. It's opposite to Invertible matrix, whose determinant is $\neq$ 0

Skew Symmetric Matrix: $A^T=-A$

edited by
Answer:

Related questions

9 votes
9 votes
1 answer
1
jaiganeshcse94 asked May 31, 2016
2,329 views
If the two matrices $\begin{bmatrix} 1 &0 &x \\ 0 & x& 1\\ 0 & 1 & x \end{bmatrix}$ and $\begin{bmatrix} x &1 &0 \\ x & 0& 1\\ 0 & x & 1 \end{bmatrix}$ have the same dete...
0 votes
0 votes
0 answers
3