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Mathematics
Orthogonal matrix
If A is an orthogonal matrix, then value of \[|A|\] is equal to
a) \[ \pm 3\]
b) \[ \pm 4\]
c) \[ \pm 2\]
d) \[ \pm 1\]
Mathematics
Orthogonal matrix
If $P$ is an orthogonal matrix and $Q=PA{{P}^{T}}$ and $B={{P}^{T}}{{Q}^{1000}}P$, then ${{B}^{-1}}$ is, where $A$ is involuntary matrix:
(A) $A$
(B) ${{A}^{1000}}$
(C) $I$
(D) None of these
Mathematics
Orthogonal matrix
A square matrix A is said to be orthogonal $AA' = A'A = {I_n}$. If A and B are orthogonal matrices, of the same size, then which one of the following is an orthogonal matrix:
A) AB
B) A+B
C) A+iB
D) i(A+B)

Mathematics
Orthogonal matrix
A skew-symmetric matrix $M$ satisfies the relation ${M^2} + I = 0$, where $I$ is the unit of matrix. The $MM'$ is equal to
$A.{\text{ }}I$
$B.{\text{ }}2I$
$C.{\text{ }} - I$
$D.$ None of these
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