NDA 2023 Maths · Mathematics · Matrices · medium

If A=beginpmatrix2&-1\\3&0endpmatrix, the sum of all the entries of A^2 is

Single correct option

A=\begin{pmatrix}2&-1\\3&0\end{pmatrix}

, the sum of all the entries of

A^2

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Answer: (D) $2$

A^2=\begin{pmatrix}4-3&-2+0\\6+0&-3+0\end{pmatrix}=\begin{pmatrix}1&-2\\6&-3\end{pmatrix}

, and the sum of its entries is

1-2+6-3=2

. Squaring each entry of

A

instead gives

\begin{pmatrix}4&1\\9&0\end{pmatrix}

with sum

14

, which is the classic mistake.

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