In this worksheet, we will practice using some properties of matrix inverse.

Q1:

Consider the matrix 𝐴=−31−25. Find 𝐴.

Q2:

If 𝐴 is a matrix, which of the following is equal to 𝐴?

Q3:

If 𝐴 and 𝐵 are both nonsingular matrices, then what is the value of (𝐴𝐵)?

Q4:

If 𝐴 is a matrix, which of the following is equal to 𝐴?

Q5:

Given 𝐴=251321174321218, find 𝐴.

Q6:

Given the matrices 𝐴 and 𝐵 where 𝐴=1−230−14001 and 𝐵=1−250−14001, find 𝐴𝐵.

Without doing any further calculations, find 𝐴.

Q7:

If 𝐴 is a nonsingular square matrix, is it correct that 𝐴⋅𝐴 equals the identity matrix?

Q8:

Given that (𝐴𝐵)=165−3−3321𝐴=−2−1−3−2,, determine 𝐵.

Q9:

Given that 𝐴 and 𝐵 are invertible matrices, which of the following is the value of 𝐵⋅(𝐴𝐵)?

Q10:

Given 𝐴=111517, find 𝐴.

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