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Learn Exercise 4.5 with Free Lessons & Tips

Let A be a nonsingular square matrix of order 3 × 3. Then  is equal to

A. B. C. D.  

We know that,

Hence, the correct answer is B.

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Find adjoint of each of the matrices.

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Verify A (adj A) = (adj AA = I .

 

 

 

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For the matrix, find the numbers a and b such that A2 + aA + bI O.

We have:

Comparing the corresponding elements of the two matrices, we have:

Hence, −4 and 1 are the required values of a and b respectively.

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If A is an invertible matrix of order 2, then det (A−1) is equal to

A. det (A) B. C. 1 D. 0

 

Since A is an invertible matrix,

Hence, the correct answer is B.

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Find adjoint of each of the matrices.

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Verify A (adj A) = (adj AA = I .

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Find the inverse of each of the matrices (if it exists).

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Find the inverse of each of the matrices (if it exists).

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Find the inverse of each of the matrices (if it exists).

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Find the inverse of each of the matrices (if it exists).

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Find the inverse of each of the matrices (if it exists).

.

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Find the inverse of each of the matrices (if it exists).

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Let and. Verify that 

From (1) and (2), we have:

(AB)−1 = B−1A−1

Hence, the given result is proved.

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If, show that. Hence find.

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For the matrixshow that A3 − 6A2 + 5A + 11 I = O. Hence, find A−1

From equation (1), we have:

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If verify that A3 − 6A2 + 9A − 4I = O and hence find A−1

From equation (1), we have:

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