Let A = \(\begin{pmatrix}2&-2\\1&-1\end{pmatrix}\) and B =\(\begin{p

1.	Let A = \(\begin{pmatrix}2&-2\\1&-1\end{pmatrix}\) and B =\(\begin{pmatrix}-1&2\\-1&2\end{pmatrix}\)Then the number of elements in the set {(n,m) : n,m \(\in\){1,2,.....,10} and nAn + mBm = 1 is ____
Answer» Correct answer is 1 A² = A and B² = B Therefore equation nAⁿ + mB^m = I becomes nA + mB = I, which gives m = n = 1 Only one set possible

Let A = \(\begin{pmatrix}2&-2\\1&-1\end{pmatrix}\) and B =\(\begin{pmatrix}-1&2\\-1&2\end{pmatrix}\)Then the number of elements in the set {(n,m) : n,m \(\in\){1,2,.....,10} and nAn + mBm = 1 is ____

Answer»

Correct answer is 1

A² = A and B² = B

Therefore equation nAⁿ + mB^m = I becomes

nA + mB = I, which gives m = n = 1

Only one set possible

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Let A = \(\begin{pmatrix}2&amp;-2\\1&amp;-1\end{pmatrix}\) and B =\(\begin{pmatrix}-1&amp;2\\-1&amp;2\end{pmatrix}\)Then the number of elements in the set {(n,m) : n,m \(\in\){1,2,.....,10} and nAn + mBm = 1 is ____

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Let A = \(\begin{pmatrix}2&-2\\1&-1\end{pmatrix}\) and B =\(\begin{pmatrix}-1&2\\-1&2\end{pmatrix}\)Then the number of elements in the set {(n,m) : n,m \(\in\){1,2,.....,10} and nAn + mBm = 1 is ____