Inverses of Matrices (Edexcel A-Level Further Mathematics): Quizzes

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Inverses of Matrices
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What is the result when a matrix AA is multiplied by its inverse A−1A^{-1}?

The identity matrix II

What condition must be met for a matrix to have an inverse?

Its determinant must be non-zero

What is a matrix with zero determinant called?

Singular

For A=(abcd)A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}, what is det(A)\text{det}(A)?

ad−bcad - bc

In the 2×22 \times 2 inverse formula, which elements swap positions?

aa and dd (diagonal elements)

What is the adjugate of a matrix?

Transpose of the cofactor matrix

What pattern is used to form the matrix of cofactors from minors?

Checkerboard pattern of signs

If AA and BB are invertible, what is (AB)−1(AB)^{-1}?

B−1A−1B^{-1}A^{-1}

To solve AX=BAX = B for XX, what is the solution using the inverse?

X=A−1BX = A^{-1}B

What type of matrices can have an inverse?

Only square matrices

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Properties of Matrices

Transformations using Matrices

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Properties of Matrices

Transformations using Matrices

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Properties of Matrices

Transformations using Matrices

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Properties of Matrices

Transformations using Matrices

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