NDA 2023 Maths · Mathematics · Matrices · hard

Let A=beginpmatrix1&2\\0&1endpmatrix and B=beginpmatrix1&0\\2&1endpmatrix. The determinant of AB-BA is

Single correct option

Let

A=\begin{pmatrix}1&2\\0&1\end{pmatrix}

and

B=\begin{pmatrix}1&0\\2&1\end{pmatrix}

. The determinant of

AB-BA

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Answer: (D) $-16$

AB=\begin{pmatrix}5&2\\2&1\end{pmatrix}

and

BA=\begin{pmatrix}1&2\\2&5\end{pmatrix}

, so

AB-BA=\begin{pmatrix}4&0\\0&-4\end{pmatrix}

with determinant

-16

. Assuming

AB=BA

would give

0

, which is the trap: matrix multiplication is not commutative.

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