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If A and B are square matrices of order 2, then det (A + B) = 0 is possible only when
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If A is a square matrix such that A (adj A) 5I, where I denotes the identity matrix of the same order. Then, find the value of |A|.
Concept: undefined >> undefined
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If A is a square matrix of order 3 such that |A| = 5, write the value of |adj A|.
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If A is a square matrix of order 3 such that |adj A| = 64, find |A|.
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If A is a non-singular square matrix such that |A| = 10, find |A−1|.
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If A is a non-singular square matrix such that \[A^{- 1} = \begin{bmatrix}5 & 3 \\ - 2 & - 1\end{bmatrix}\] , then find \[\left( A^T \right)^{- 1} .\]
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If A is a square matrix of order 3 such that |A| = 2, then write the value of adj (adj A).
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If A is a square matrix of order 3 such that |A| = 3, then write the value of adj (adj A).
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If A is a square matrix of order 3 such that adj (2A) = k adj (A), then write the value of k.
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Let A be a 3 × 3 square matrix, such that A (adj A) = 2 I, where I is the identity matrix. Write the value of |adj A|.
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If A is a square matrix such that \[A \left( adj A \right) = \begin{bmatrix}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{bmatrix}\] , then write the value of |adj A|.
Concept: undefined >> undefined
Let A be a square matrix such that \[A^2 - A + I = O\], then write \[A^{- 1}\] interms of A.
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If A and B are square matrices such that B = − A−1 BA, then (A + B)2 = ________ .
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If \[A = \begin{bmatrix}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{bmatrix},\text{ then }A^5 =\] ____________ .
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If A is a square matrix such that A2 = I, then A−1 is equal to _______ .
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Find the differential equation of all the circles which pass through the origin and whose centres lie on y-axis.
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Find the differential equation of all the circles which pass through the origin and whose centres lie on x-axis.
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Form the differential equation having \[y = \left( \sin^{- 1} x \right)^2 + A \cos^{- 1} x + B\], where A and B are arbitrary constants, as its general solution.
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If y = sin x and x changes from π/2 to 22/14, what is the approximate change in y ?
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