Solution.
A=⎝⎛31313161−6261−21021⎠⎞
An orthogonal matrix is a nondegenerate square matrix A (usually with real elements) such that
AAT=ATA=I, where AT is transposed matrix to matrix A, and I is the identity matrix.
detA=−31−61−31−61=−1=0.
AT=⎝⎛3161−2131−620316121⎠⎞AAT=⎝⎛31313161−6261−21021⎠⎞⋅⎝⎛3161−2131−620316121⎠⎞==⎝⎛100010001⎠⎞=I.ATA=I. Answer. Yes, A is orthogonal matrix.
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