If $$X = \left[ {\matrix{ 3 & { - 4} \cr 1 & { - 1} \cr } } \right]$$, $$B = \left[ {\matrix{ 5 & 2 \cr { - 2} & 1 \cr } } \right]$$ and $$A = \left[ {\matrix{ p & q \cr r & s \cr } } \right]$$ satisfy the equation AX = B, then the matrix A is equal to

Let $$A = \left[ {\matrix{ {x + y} & y \cr {2x} & {x - y} \cr } } \right]$$, $$B = \left[ {\matrix{ 2 \cr { - 1} \cr } } \right]$$ and $$C = \left[ {\matrix{ 3 \cr 2 \cr } } \right]$$. If AB = C, then what is A² equal to?

If $$E(\theta ) = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$, then E($$\alpha$$) E($$\beta$$) is equal to

If A is an orthogonal matrix of order 3 and $$B = \left[ {\matrix{ 1 & 2 & 3 \cr { - 3} & 0 & 2 \cr 2 & 5 & 0 \cr } } \right]$$, then which of the following is/are correct?

1. $$\left| {AB} \right| = \pm \,47$$ 2. AB = BA

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