Let `A`
be a `3xx3`
square matrix such that
`A(a d j\ A)=2I`
, where `I`
is the identity matrix.
Write the value of `|a d j\ A|`
.
Text Solution
Verified by Experts
Consider the following identity A(adjA)=∣A∣I.
Thus comparing it with the above equation gives us `∣A∣=2`
Now `∣adjA∣=∣A∣^(n−1)`
where n is the order of the square matrix.
Here 'n' is 3, therefore,
`∣adjA∣=∣A∣^(3−1)=∣A∣^2=2^2=4`.
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Knowledge Check
Let A be a square matrix of order 2 such that A-1 = AA^(T) (where I is an identity matrix of order 2), then which one of the following is INCORRECT statement (where |A| represents determinant value of matrix A)
A
|A|=1
B
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C
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A is a 2xx2 matrix, such that A={:[(a_(ij))]:} , where a_(ij)=2i-j+1 . The matrix A is
A
`{:[(2,1),(4,3)]:}`
B
`{:[(2,4),(3,1)]:}`
C
`{:[(2,3),(4,1)]:}`
D
`{:[(1,4),(3,2)]:}`
If for a 2xx2 matrix A,A^(2)+I=O , where I is identity matrix then A equals
A
`[(1,0),(0,1)]`
B
`[(-i,0),(0,-i)]`
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`[(1,2),(-1,1)]`
D
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