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GradeOrthogonal Matrix

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If A is an orthogonal matrix, then value of \[|A|\] is equal to

a) \[ \pm 3\]

b) \[ \pm 4\]

c) \[ \pm 2\]

d) \[ \pm 1\]

a) \[ \pm 3\]

b) \[ \pm 4\]

c) \[ \pm 2\]

d) \[ \pm 1\]

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

(A) $A$

(B) ${{A}^{1000}}$

(C) $I$

(D) None of these

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)

A) AB

B) A+B

C) A+iB

D) i(A+B)

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

$A.{\text{ }}I$

$B.{\text{ }}2I$

$C.{\text{ }} - I$

$D.$ None of these

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