Find adjoint of each of the matrices in Exercises 1 and 2.
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Verify A (adj A) = (adj A) A = |A| I in Exercises 3 and 4
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Find the inverse of each of the matrices (if it exists) given in Exercises 5 to 11.
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Verify that (AB)^{–1} = B^{–1} A^{–1} | |

show that A^{2} – 5A + 7I = O. Hence find A^{–1} | |

14. For the matrix find the numbers a and b such that A^{2} + aA + bI = O | |

15. For the matrix Show that A^{3}– 6A^{2} + 5A + 11 I = O. Hence, find A^{–1} | |

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17. Let A be a nonsingular square matrix of order 3 × 3. Then |adj A| is equal to (A) |A| (B) |A|^{2} (C) |A|^{3} (D) 3|A| | |

18. If A is an invertible matrix of order 2, then det (A^{–1}) is equal to (A) det (A) (B)1/det (A) (C) 1 (D) 0 | |