If A and B are square matrices of same order, then which of the following statements is/are always true? (i) (A + B)(A − B) = A² − B² (ii) AB = BA (iii) (A + B)² = A² + AB + BA + B² (iv) AB = 0 ⇒ A = 0 or B = 0

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Properties of Matrix Multiplication, Non-Commutativity of Matrix Multiplication | PadhAiPro

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MCQ (Single)Properties of Matrix MultiplicationNon-Commutativity 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 A = [1 2 3; 3 −2 1; 4 2 1], then show that A³ − 23A − 40I = O.

For two matrices A and B, given that A⁻¹ = (1/4)B, then inverse of (4A) is :