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question_answer1) If three matrices Then
question_answer2) If A is a square matrix of order 3 such that , then find \[\left| adj.A \right|.\]
question_answer3) If \[{{A}^{2}}=A\] and \[{{\left( I+A \right)}^{4}}\] is equal to \[I+kA\] then find k.
question_answer4) If and \[C=5A,\]the find\[\frac{\left| adj\,\,B \right|}{\left| C \right|}\].
question_answer5) If and \[UV+XY=\left[ k \right]\]then find k.
question_answer6) If A is a square matrix of order n such that \[\left| adj\,\left( adj\,\,A \right)\, \right|={{\left| A \right|}^{9}},\]then find the value of n.
question_answer7) If \[P=\left[ \begin{matrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \\ \end{matrix} \right],A=\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right],Q=PA{{P}^{T}}\]and \[{{P}^{T}}{{Q}^{2005}}P=\left[ \begin{matrix} 1 & k \\ 0 & 1 \\ \end{matrix} \right]\] then find k.
question_answer8) If and I is a unit matrix of 3rd order then find the element \[{{a}_{22}}\]of\[\left( {{A}^{2}}+9I \right)\].
question_answer9) In a symmetric matrix of order '12' find maximum number of different elements.
question_answer10) A is a \[2\times 2\] matrix such thatand find the sum of the elements of A.
question_answer11) Let and \[\left| A \right|=1,\,\,abc=1,\]then find the value of\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\].
question_answer12) Find the sum of the values of x satisfying the equation
question_answer13) If \[A=\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\] and \[{{A}^{100}}\] is equal to \[{{2}^{k}}A\] then find k.
question_answer14) If \[A=\left[ \begin{matrix} 1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \\ \end{matrix} \right]\] and det \[\left[ adj\,\,A \right]\] is equal to \[{{k}^{\lambda }}\] then find \[\left( k+\lambda \right)\].
question_answer15) The number of different matrices can be formed using 12 different real numbers is \[m\left( 12 \right)!\] then find the value of m.
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