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The determinant of which of the following matrices is a perfect square ?

A. [529−16]\begin{bmatrix}5&29\\-1&6\end{bmatrix}

B. [52616]\begin{bmatrix}5&26\\1&6\end{bmatrix}

C. [1031710]\begin{bmatrix}10&3\\17&10\end{bmatrix}

D. [85−3−8]\begin{bmatrix}8&5\\-3&-8\end{bmatrix}

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 3

The determinants are A: 30+29=5930+29=59; B: 30−26=430-26=4; C: 100−51=49100-51=49; D: −64+15=−49-64+15=-49. Only 4 and 49 are perfect squares, so B and C qualify (a negative value cannot be a perfect square).

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