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If A–1 = \(\begin{bmatrix}3&-1&1\\-15&6&-5\\5&-2&2\end{bmatrix}\)and B = \(\begin{bmatrix}1&2&-2\\-1&3&0\\0&-2&1\end{bmatrix}\), find (AB)–1.

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  A–1 = \(\begin{bmatrix}3&-1&1\\-15&6&-5\\5&-2&2\end{bmatrix}\)and B = \(\begin{bmatrix}1&2&-2\\-1&3&0\\0&-2&1\end{bmatrix}\)

|B| = 1(3 – 0) – 2( – 1 – 0) – 2(2 – 0)

= 3 + 2 – 4

|B| = 1

Now, B–1\(\frac{1}{|B|}adjB\)

Cofactors of B are:

C11 = – 3 C21 = 2 C31 = 6

C12 = 1 C22 = 1 C32 = 2

C13 = 2 C23 = 2 C33 = 5

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