Let A = (2 - 2 1 - 1) and B = (- 1 2 - 1 2). Then the number of elements in the set (n, m): n, m 1, 2,.........., 10 and nAⁿ + mB^(m) = I is _ _ _ _ _ _.

Matrices and Determinants: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Evening shift · Q42

JEE Main 202225 Jun, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

A = \left( {\matrix{ 2 & { - 2} \cr 1 & { - 1} \cr } } \right)

and

B = \left( {\matrix{ { - 1} & 2 \cr { - 1} & 2 \cr } } \right)

. Then the number of elements in the set {(n, m) : n, m

\in

{1, 2, .........., 10} and nA^n + mB^m = I} is ____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2022 · 25 Jun, Evening shift · Q42

JEE Main 202225 Jun, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

A = \left( {\matrix{ 2 & { - 2} \cr 1 & { - 1} \cr } } \right)

and

B = \left( {\matrix{ { - 1} & 2 \cr { - 1} & 2 \cr } } \right)

. Then the number of elements in the set {(n, m) : n, m

\in

{1, 2, .........., 10} and nA^n + mB^m = I} is ____________.

Your answerType your answer. Integers and decimals are accepted.