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In this worksheet, we will practice using the matrix multiplication to determine the square and cube of a square matrix.

Q1:

Consider the matrix 𝐴=112101210.

Find 𝐴.

Find 𝐴.

Q2:

Which of the following represents a matrix 𝐴 such that 𝐴=𝐼, yet 𝐴≠𝐼 and 𝐴≠−𝐼?

Q3:

For 𝐴=4−54−5, write 𝐴 as a multiple of 𝐴.

Q4:

Which of the following statements is true for all 𝑛×𝑛 matrices 𝐴 and 𝐵?

Q5:

Consider 𝑋=−3−35−6,𝑌=136−6. What is 𝑋−𝑌?

Q6:

Given that 𝐴=−61−55, find 𝐴.

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