If matrix A = [[3, 3], [-3, -3]] and A² = λA, then write the value of λ.

If A = [[3, 3], [-3, -3]], then A² can be computed as shown below:
A² = [[3, 3], [-3, -3]] * [[3, 3], [-3, -3]] = [[33 + 3(-3), 33 + 3(-3)], [-33 + (-3)(-3), -33 + (-3)(-3)]] = [[9 - 9, 9 - 9], [-9 + 9, -9 + 9]] = [[0, 0], [0, 0]]
Since A² = λA, therefore, [[0, 0], [0, 0]] = λ[[3, 3], [-3, -3]]
[[0, 0], [0, 0]] = [[3λ, 3λ], [-3λ, -3λ]]
Now equating the matrices we get 3λ = 0 => λ = 0.