If A = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix}, find A^2 - 5A + 6I, where I is the identity matrix of order 2.

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Identity Matrix, Multiplication of a Matrix by a Scalar, Properties of Matrix Multiplication | PadhAiPro

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TextIdentity MatrixMultiplication of a Matrix by a ScalarProperties of Matrix Multiplication

If A and B are two non-zero square matrices of same order such that (A + B)² = A² + B², then :

If F(x) = [cos x –sin x 0; sin x cos x 0; 0 0 1] and [F(x)]² = F(kx), then the value of k is :

Matrix Multiplication and Its Conditions

Properties of Matrix Multiplication

If A = [2 1; -4 -2], then the value of I – A + A² – A³ + ... is:

If A = [1 0 2; 0 2 1; 2 0 3], then show that A³ − 6A² + 7A + 2I = O.

If x[1 2] + y[2 5] = [4 9], then :

If A is a square matrix and A² = A, then (I + A)² - 3A is equal to :