Let A be 3 - 3 scalar matrix such that aii - 3 and B is matrix of 3 - 3 order whose determinant is 9- the value of det A adj - Bis

The correct option is D 3^7 We know that #160; det (A (adj B)) = (det A) (det (adj B)) #160; #160; =(3)^3 (det (B))^2 #160; #160; ...

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Standard XII

Mathematics

Orthogonal Matrix

Let A be 3 ...

Question

Let A be 3 $\times$ 3 scalar matrix such that $a_{i i} = 3$ and B is matrix of 3 $\times$ 3 order whose determinant is 9, the value of det (A (adj . B))
is

3^{4}

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3^{6}

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3^{7}

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3^{8}

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Solution

The correct option is D $3^{7}$
We know that
$d e t (A (a d j B)) = (d e t A) (d e t (a d j B))$
$= (3)^{3} (d e t (B))^{2}$
$= 27 \times (9)^{2}$
$= 3^{7}$

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Let A be 3 × 3 scalar matrix such that aii=3 and B is matrix of 3 × 3 order whose determinant is 9, the value of det (A (adj . B))is

The correct option is D 37We know that det(A(adjB))=(detA)(det(adjB)) =(3)3(det(B))2 =27×(9)2 =37

Let A be 3 $\times$ 3 scalar matrix such that $a_{i i} = 3$ and B is matrix of 3 $\times$ 3 order whose determinant is 9, the value of det (A (adj . B))
is

The correct option is D $3^{7}$
We know that
$d e t (A (a d j B)) = (d e t A) (d e t (a d j B))$
$= (3)^{3} (d e t (B))^{2}$
$= 27 \times (9)^{2}$
$= 3^{7}$