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Question: If A = \(\begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}\), then A<sup>–1</sup> is equal to...

If A = [1235]\begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}, then A–1 is equal to

A

[5231]\begin{bmatrix} 5 & 2 \\ 3 & 1 \end{bmatrix}

B

[–532–1]\begin{bmatrix} –5 & 3 \\ 2 & –1 \end{bmatrix}

C

[–523–1]\begin{bmatrix} –5 & 2 \\ 3 & –1 \end{bmatrix}

D

None of these

Answer

[–523–1]\begin{bmatrix} –5 & 2 \\ 3 & –1 \end{bmatrix}

Explanation

Solution

A–1 = adj 6muA∣A∣\frac{adj\mspace{6mu} A}{|A|}

Q |A| = – 1

adj A = [5–2–31]\begin{bmatrix} 5 & –2 \\ –3 & 1 \end{bmatrix}

so, A–1 = [–523–1]\begin{bmatrix} –5 & 2 \\ 3 & –1 \end{bmatrix}