Find the number of all possible ordered sets of two n- n matrices A and B for which AB-BA- I-

The correct option is D Zero AB BA=I Let a n× n matrix. Take trace of both sides. trace (AB BA)=trace (I) trace (AB) trace (BA)=n ...

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Standard XII

Mathematics

Multiplication of Matrices

Find the numb...

Question

Find the number of all possible ordered sets of two $(n \times n)$ matrices A and B for which $A B - B A =$ $I$ .

Infinite

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n^{2}

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n!

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Zero

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Solution

The correct option is D Zero
$A B - B A = I$

Let a $n \times n$ matrix. Take trace of both sides. trace $(A B - B A) = t r a c e (I)$

trace $(A B) -$ trace $(B A) = n$

$\Rightarrow n = 0$

so zero possible ordered let of two $(n \times n)$ matrix.

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Find the number of all possible ordered sets of two (n×n) matrices A and B for which AB−BA=I.

The correct option is D ZeroAB−BA=ILet a n×n matrix. Take trace of both sides. trace (AB−BA)=trace (I)trace (AB)−trace (BA)=n⇒ n=0so zero possible ordered let of two (n×n) matrix.

Find the number of all possible ordered sets of two $(n \times n)$ matrices A and B for which $A B - B A =$ $I$ .

The correct option is D Zero
$A B - B A = I$

Let a $n \times n$ matrix. Take trace of both sides. trace $(A B - B A) = t r a c e (I)$

trace $(A B) -$ trace $(B A) = n$

$\Rightarrow n = 0$

so zero possible ordered let of two $(n \times n)$ matrix.