Matrices as rectangular arrays; equality; addition; scalar multiplication; product; transpose; elementary row/column transformations; determinant of a square matrix of order up to three; adjoint; inverse; properties; diagonal, symmetric, skew-symmetric matrices; solution of simultaneous linear equations in two or three variables.
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Q1 · Matrices · MEDIUM
If A = [[2, 3], [1, 2]] and A⁻¹ = aA + bI, then the values of a and b are:
Q2 · Matrices · HARD
Let A be a 3×3 matrix such that A³ - 5A² + 7A - 3I = O, where I is the identity matrix and O is the null matrix. If A⁻¹ exists, then A⁻¹ equals: