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Scalar Matrix

If A is ortho...

Question

If A is orthogonal matrix of order 2 then det(adj 2A) =

(a) 4 (b) 16. (c) 27 (d) 64

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Solution

We know that,
det of an orthogonal matrix = -1 or +1
det (A) = +1 or -1
Since A is of order 2,
det (2A) = 4×det (A)
= +4 or -4

Also we know the formula,
det (adj A)
= [det (A)]^n-1
where n is the order of the matrix.

So, det (adj 2A)
= [det (2A)]^2-1
= 4^1 or (-4)^1
= +4 or -4

Answer is option (a) 4

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