PrepBharat

1. The inverse of a symmetric matrix (if it exists) is
a) a symmetric matrix
b) a skew symmetric matrix
c) a diagonal matrix
d) none of these

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2. The inverse of a skew symmetric matrix (if it exists) is
a) a symmetric matrix
b) a skew symmetric matrix
c) a diagonal matrix
d) none of these

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3. The inverse of a skew symmetric matrix of odd order is
a) a symmetric matrix
b) a skew symmetric matrix
c) diagonal matrix
d) does not exist

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4. If A is an orthogonal matrix, then |A| is
a) 1
b) -1
c) \[\pm1\]
d) 0

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5. If A is a \[3\times3\]  non-singular matrix, then adj (adj A) is equal to
a) \[\mid A\mid A\]
b) \[\mid A\mid^{2} A\]
c) \[\mid A\mid^{-1} A\]
d) 0

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6. If A and B are two square matrices such that \[B=-A^{-1} BA\]   , then \[\left(A+B \right)^{2} \]   is equal to
a) O
b) \[A^{2}+B^{2} \]
c) \[A^{2}+2AB+B^{2} \]
d) A+B

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7. If \[A=\begin{bmatrix}\alpha & \beta \\\gamma & -\alpha \end{bmatrix} \]     is such that \[A^{2}=I \] , then
a) \[1+\alpha^{2}+\beta\gamma=0\]
b) \[1-\alpha^{2}-\beta\gamma=0\]
c) \[1-\alpha^{2}+\beta\gamma=0\]
d) \[1+\alpha^{2}-\beta\gamma=0\]

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8. The value of x for which the matrix \[A=\begin{bmatrix}2 & 0 & 7 \\0 & 1 & 0 \\1 & -2 & 1\end{bmatrix}\]     is inverse of \[B=\begin{bmatrix}-x & 14x & 7x \\0 & 1 & 0 \\x & -4x & -2x\end{bmatrix}\]
is
a) \[\frac{1}{2}\]
b) \[\frac{1}{3}\]
c) \[\frac{1}{4}\]
d) \[\frac{1}{5}\]

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9. If \[A\left(\alpha,\beta\right)=\begin{bmatrix}\cos\alpha & \sin\alpha & 0 \\-\sin\alpha & \cos\alpha & 0 \\0 & 0 & e^{\beta}\end{bmatrix}\]     , then \[A\left(\alpha,\beta\right)^{-1}\]   is equal to
a) \[A\left(-\alpha,\beta\right)\]
b) \[A\left(-\alpha,-\beta\right)\]
c) \[A\left(\alpha,-\beta\right)\]
d) \[A\left(\alpha,\beta\right)\]

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10. If A is a \[3\times 3\]  skew-symmetric matrix, then trace of A is equal to
a) 1
b) 3
c) -1
d) \[\mid A\mid\]

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