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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.
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.
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.
Let 
and
. Verify that 
From (1) and (2), we have:
(AB)−1 = B−1A−1
Hence, the given result is proved.
For the matrix
show that A3 − 6A2 + 5A + 11 I = O. Hence, find A−1
From equation (1), we have:
If 
verify that A3 − 6A2 + 9A − 4I = O and hence find A−1
From equation (1), we have:
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I .
I .
. 
, show that
. Hence find
. 
