Given a square matrix A of order 3 such that A² = [3 –4 4; 0 –1 0; –2 2 –3], show that A³ = A⁻¹.

Matrix Multiplication and Its Conditions, Inverse of a Square Matrix Using Adjoint | PadhAiPro

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TextMatrix Multiplication and Its ConditionsInverse of a Square Matrix Using AdjointCBSE PYQ

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

If A = [1 –2 0; 2 –1 –1; 0 –2 1], find A⁻¹ and use it to solve the following system of equations : x – 2y = 10, 2x – y – z = 8, – 2y + z = 7

Inverse of a Square Matrix Using Adjoint

Solving System of Linear Equations Using Inverse of Matrix

If A = [–1 a 2; 1 2 x; 3 1 1] and A⁻¹ = [1 –1 1; –8 7 –5; b y 3], find the value of (a + x) – (b + y).

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 :

Solve the following system of equations, using matrices : 2/x + 3/y + 10/z = 4, 4/x – 6/y + 5/z = 1, 6/x + 9/y – 20/z = 2 where x, y, z ≠ 0

If A = [1 cot x; –cot x 1], show that A′A⁻¹ = [–cos 2x –sin 2x; sin 2x –cos 2x].